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 closer 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.
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