er together; that is to say, when the
compressed gaseous mass occupies a more and more restricted volume. On
the other hand, we assimilate the molecules, as a first approximation,
to material points without dimensions; in the evaluation of the path
traversed by each molecule no notice is taken of the fact that, at the
moment of the shock, their centres of gravity are still separated by a
distance equal to twice the radius of the molecule.

M. Van der Waals has sought out the modifications which must be
introduced into the simple characteristic equation to bring it nearer
to reality. He extends to the case of gases the considerations by
which Laplace, in his famous theory of capillarity, reduced the effect
of the molecular attraction to a perpendicular pressure exercised on
the surface of a liquid. This leads him to add to the external
pressure, that due to the reciprocal attractions of the gaseous
particles. On the other hand, when we attribute finite dimensions to
these particles, we must give a higher value to the number of shocks
produced in a given time, since the effect of these dimensions is to
diminish the mean path they traverse in the time which elapses between
two consecutive shocks.

The calculation thus pursued leads to our adding to the pressure in
the simple equation a term which is designated the internal pressure,
and which is the quotient of a constant by the square of the volume;
also to our deducting from the volume a constant which is the
quadruple of the total and invariable volume which the gaseous
molecules would occupy did they touch one another.

The experiments fit in fairly well with the formula of Van der Waals,
but considerable discrepancies occur when we extend its limits,
particularly when the pressures throughout a rather wider interval are
considered; so that other and rather more complex formulas, on which
there is no advantage in dwelling, have been proposed, and, in certain
cases, better represent the facts.

But the most remarkable result of M. Van der Waals' calculations is
the discovery of corresponding states. For a long time physicists
spoke of bodies taken in a comparable state. Dalton, for example,
pointed out that liquids have vapour-pressures equal to the
temperatures equally distant from their boiling-point; but that if, in
this particular property, liquids were comparable under these
conditions of temperature, as regards other properties the parallelism
was no longer t