g different bodies which happen to be in the same
conditions of temperature and pressure, but in very different
conditions as regards their critical points.

From the experimental point of view, M. Amagat has been able, with
extreme skill, to conquer the most serious difficulties. He has
managed to measure with precision pressures amounting to 3000
atmospheres, and also the very small volumes then occupied by the
fluid mass under consideration. This last measurement, which
necessitates numerous corrections, is the most delicate part of the
operation. These researches have dealt with a certain number of
different bodies. Those relating to carbonic acid and ethylene take in
the critical point. Others, on hydrogen and nitrogen, for instance,
are very extended. Others, again, such as the study of the
compressibility of water, have a special interest, on account of the
peculiar properties of this substance. M. Amagat, by a very concise
discussion of the experiments, has also been able to definitely
establish the laws of compressibility and dilatation of fluids under
constant pressure, and to determine the value of the various
coefficients as well as their variations. It ought to be possible to
condense all these results into a single formula representing the
volume, the temperature, and the pressure. Rankin and, subsequently,
Recknagel, and then Hirn, formerly proposed formulas of that kind; but
the most famous, the one which first appeared to contain in a
satisfactory manner all the facts which experiments brought to light
and led to the production of many others, was the celebrated equation
of Van der Waals.

Professor Van der Waals arrived at this relation by relying upon
considerations derived from the kinetic theory of gases. If we keep to
the simple idea at the bottom of this theory, we at once demonstrate
that the gas ought to obey the laws of Mariotte and of Gay-Lussac, so
that the characteristic equation would be obtained by the statement
that the product of the number which is the measure of the volume by
that which is the measure of the pressure is equal to a constant
coefficient multiplied by the degree of the absolute temperature. But
to get at this result we neglect two important factors.

We do not take into account, in fact, the attraction which the
molecules must exercise on each other. Now, this attraction, which is
never absolutely non-existent, may become considerable when the
molecules are drawn clos