lculations, but its sensibility is unequally distributed over the
different regions of the diagram. M. Raveau has pointed out an equally
simple way of verifying the law, by remarking that if the logarithms
of the pressure and volume are taken as co-ordinates, the co-ordinates
of two corresponding points differ by two constant quantities, and the
corresponding curves are identical.

From these comparisons, and from other important researches, among
which should be particularly mentioned those of Mr S. Young and M.
Mathias, it results that the laws of corresponding states have not,
unfortunately, the degree of generality which we at first attributed
to them, but that they are satisfactory when applied to certain groups
of bodies.[7]

[Footnote 7: Mr Preston thus puts it: "The law [of corresponding
states] seems to be not quite, but very nearly true for these
substances [_i.e._ the halogen derivatives of benzene]; but in the
case of the other substances examined, the majority of these
generalizations were either only roughly true or altogether departed
from" (_Theory of Heat_, London, 1904, p. 514.)--ED.]

If in the study of the statics of a simple fluid the experimental
results are already complex, we ought to expect much greater
difficulties when we come to deal with mixtures; still the problem has
been approached, and many points are already cleared up.

Mixed fluids may first of all be regarded as composed of a large
number of invariable particles. In this particularly simple case M.
Van der Waals has established a characteristic equation of the
mixtures which is founded on mechanical considerations. Various
verifications of this formula have been effected, and it has, in
particular, been the object of very important remarks by M. Daniel
Berthelot.

It is interesting to note that thermodynamics seems powerless to
determine this equation, for it does not trouble itself about the
nature of the bodies obedient to its laws; but, on the other hand, it
intervenes to determine the properties of coexisting phases. If we
examine the conditions of equilibrium of a mixture which is not
subjected to external forces, it will be demonstrated that the
distribution must come back to a juxtaposition of homogeneous phases;
in a given volume, matter ought so to arrange itself that the total
sum of free energy has a minimum value. Thus, in order to elucidate
all questions relating to the number and qualities of the phases into
whic