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.
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