s. He thus discovered over again the famous law on the lowering
of the congelation temperature of solvents which had just been
established by M. Raoult after a long series of now classic
researches.

[Footnote 14: The "second principle" referred to has been thus
enunciated: "In every engine that produces work there is a fall of
temperature, and the maximum output of a perfect engine--_i.e._ the
ratio between the heat consumed in work and the heat supplied--depends
only on the extreme temperatures between which the fluid is
evolved."--Demanet, _Notes de Physique Experimentale_, Louvain, 1905,
fasc. 2, p. 147. Clausius put it in a negative form, as thus: No
engine can of itself, without the aid of external agency, transfer
heat from a body at low temperature to a body at a high temperature.
Cf. Ganot's _Physics_, 17th English edition, Sec. 508.--ED.]

In the minds of many persons, however, grave doubts persisted.
Solution appeared to be an essentially irreversible phenomenon. It was
therefore, in all strictness, impossible to calculate the entropy of a
solution, and consequently to be certain of the value of the
thermodynamic potential. The objection would be serious even to-day,
and, in calculations, what is called the paradox of Gibbs would be an
obstacle.

We should not hesitate, however, to apply the Phase Law to solutions,
and this law already gives us the key to a certain number of facts. It
puts in evidence, for example, the part played by the eutectic point--
that is to say, the point at which (to keep to the simple case in
which we have to do with two bodies only, the solvent and the solute)
the solution is in equilibrium at once with the two possible solids,
the dissolved body and the solvent solidified. The knowledge of this
point explains the properties of refrigerating mixtures, and it is
also one of the most useful for the theory of alloys. The scruples of
physicists ought to have been removed on the memorable occasion when
Professor Van t'Hoff demonstrated that solution can operate reversibly
by reason of the phenomena of osmosis. But the experiment can only
succeed in very rare cases; and, on the other hand, Professor Van
t'Hoff was naturally led to another very bold conception. He regarded
the molecule of the dissolved body as a gaseous one, and assimilated
solution, not as had hitherto been the rule, to fusion, but to a kind
of vaporization. Naturally his ideas were not immediately accepted by
the sc