and of a certain number of definite combinations. Their
composition may thus be very complex: but Gibbs' rule gives us at once
important information on the point, since it indicates that there
cannot exist, in general, more than two distinct solutions in an alloy
of two metals.

Solid alloys may be classed like liquid ones. Two metals or more
dissolve one into the other, and form a solid solution quite analogous
to the liquid solution. But the study of these solid solutions is
rendered singularly difficult by the fact that the equilibrium so
rapidly reached in the case of liquids in this case takes days and, in
certain cases, perhaps even centuries to become established.

CHAPTER V

SOLUTIONS AND ELECTROLYTIC DISSOCIATION

Sec. 1. SOLUTION

Vaporization and fusion are not the only means by which the physical
state of a body may be changed without modifying its chemical
constitution. From the most remote periods solution has also been
known and studied, but only in the last twenty years have we obtained
other than empirical information regarding this phenomenon.

It is natural to employ here also the methods which have allowed us to
penetrate into the knowledge of other transformations. The problem of
solution may be approached by way of thermodynamics and of the
hypotheses of kinetics.

As long ago as 1858, Kirchhoff, by attributing to saline solutions--
that is to say, to mixtures of water and a non-volatile liquid like
sulphuric acid--the properties of internal energy, discovered a
relation between the quantity of heat given out on the addition of a
certain quantity of water to a solution and the variations to which
condensation and temperature subject the vapour-tension of the
solution. He calculated for this purpose the variations of energy
which are produced when passing from one state to another by two
different series of transformations; and, by comparing the two
expressions thus obtained, he established a relation between the
various elements of the phenomenon. But, for a long time afterwards,
the question made little progress, because there seemed to be hardly
any means of introducing into this study the second principle of
thermodynamics.[14] It was the memoir of Gibbs which at last opened
out this rich domain and enabled it to be rationally exploited. As
early as 1886, M. Duhem showed that the theory of the thermodynamic
potential furnished precise information on solutions or liquid
mixture