omenon of retrograde condensation. We may say that the properties
of the critical point of a homogeneous substance are, in a way,
divided, when it is a question of a binary mixture, between the two
points mentioned.

Calculation has enabled M. Van der Waals, by the application of his
kinetic theories, and M. Duhem, by means of thermodynamics, to foresee
most of the results which have since been verified by experiment. All
these facts have been admirably set forth and systematically
co-ordinated by M. Mathias, who, by his own researches, moreover, has
made contributions of the highest value to the study of questions
regarding the continuity of the liquid and gaseous states.

The further knowledge of critical elements has allowed the laws of
corresponding states to be more closely examined in the case of
homogeneous substances. It has shown that, as I have already said,
bodies must be arranged in groups, and this fact clearly proves that
the properties of a given fluid are not determined by its critical
constants alone, and that it is necessary to add to them some other
specific parameters; M. Mathias and M. D. Berthelot have indicated
some which seem to play a considerable part.

It results also from this that the characteristic equation of a fluid
cannot yet be considered perfectly known. Neither the equation of Van
der Waals nor the more complicated formulas which have been proposed
by various authors are in perfect conformity with reality. We may
think that researches of this kind will only be successful if
attention is concentrated, not only on the phenomena of
compressibility and dilatation, but also on the calorimetric
properties of bodies. Thermodynamics indeed establishes relations
between those properties and other constants, but does not allow
everything to be foreseen.

Several physicists have effected very interesting calorimetric
measurements, either, like M. Perot, in order to verify Clapeyron's
formula regarding the heat of vaporization, or to ascertain the values
of specific heats and their variations when the temperature or the
pressure happens to change. M. Mathias has even succeeded in
completely determining the specific heats of liquefied gases and of
their saturated vapours, as well as the heat of internal and external
vaporization.

Sec. 2. THE LIQUEFACTION OF GASES, AND THE PROPERTIES OF BODIES AT A
LOW TEMPERATURE

The scientific advantages of all these researches have been great,