esent 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