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.  It was not until M. Van der Waals exhumed the memoir of Gibbs, when numerous physicists or chemists, most of them Dutch—­Professor Van t’Hoff, Bakhius Roozeboom, and others—­utilized the rules set forth in this memoir for the discussion of the most complicated chemical reactions, that the extent of the new laws was fully understood.

The chief rule of Gibbs is the one so celebrated at the present day under the name of the Phase Law.  We know that by phases are designated the homogeneous substances into which a system is divided; thus carbonate of lime, lime, and carbonic acid gas are the three phases of a system which comprises Iceland spar partially dissociated into lime and carbonic acid gas.  The number of phases added to the number of independent components—­that is to say, bodies whose mass is left arbitrary by the chemical formulas of the substances entering into the reaction—­fixes the general form of the law of equilibrium of the system; that is to say, the number of quantities which, by their variations (temperature and pressure), would be of a nature to modify its equilibrium by modifying the constitution of the phases.

Several authors, M. Raveau in particular, have indeed given very simple demonstrations of this law which are not based on thermodynamics; but thermodynamics, which led to its discovery, continues to give it its true scope.  Moreover, it would not suffice merely to determine quantitatively those laws of which it makes known the general form.  We must, if we wish to penetrate deeper into details, particularize the hypothesis, and admit, for instance, with Gibbs that we are dealing with perfect gases; while, thanks to thermodynamics, we can constitute a complete theory of dissociation which leads to formulas in complete accord with the numerical results of the experiment.  We can thus follow closely all questions concerning the displacements of the equilibrium, and find a relation of the first importance between the masses of the bodies which react in order to constitute a system in equilibrium.

The statics thus constructed constitutes at the present day an important edifice to be henceforth classed amongst historical monuments.  Some theorists even wish to go a step beyond.  They have attempted to begin by the same means a more complete study of those systems whose state changes from one moment to another.  This is, moreover, a study which is necessary to complete satisfactorily the study of equilibrium itself; for without it grave doubts would exist as to the conditions of stability, and it alone can give their true meaning to questions relating to displacements of equilibrium.

The problems with which we are thus confronted are singularly difficult.  M. Duhem has given us many excellent examples of the fecundity of the method; but if thermodynamic statics may be considered definitely founded, it cannot be said that the general dynamics of systems, considered as the study of thermal movements and variations, are yet as solidly established.