s that of the analogous
coefficient of the characteristic equation of a perfect gas. There is
in this a coincidence which has also been utilized in the preceding
thermodynamic calculations. It may be purely fortuitous, but we can
hardly refrain from finding in it a physical meaning.

Professor Van t'Hoff has considered this coincidence a demonstration
that there exists a strong analogy between a body in solution and a
gas; as a matter of fact, it may seem that, in a solution, the
distance between the molecules becomes comparable to the molecular
distances met with in gases, and that the molecule acquires the same
degree of liberty and the same simplicity in both phenomena. In that
case it seems probable that solutions will be subject to laws
independent of the chemical nature of the dissolved molecule and
comparable to the laws governing gases, while if we adopt the kinetic
image for the gas, we shall be led to represent to ourselves in a
similar way the phenomena which manifest themselves in a solution.
Osmotic pressure will then appear to be due to the shock of the
dissolved molecules against the membrane. It will come from one side
of this partition to superpose itself on the hydrostatic pressure,
which latter must have the same value on both sides.

The analogy with a perfect gas naturally becomes much greater as the
solution becomes more diluted. It then imitates gas in some other
properties; the internal work of the variation of volume is nil, and
the specific heat is only a function of the temperature. A solution
which is diluted by a reversible method is cooled like a gas which
expands adiabatically.[17]

[Footnote 17: That is, without receiving or emitting any heat.--ED.]

It must, however, be acknowledged that, in other points, the analogy
is much less perfect. The opinion which sees in solution a phenomenon
resembling fusion, and which has left an indelible trace in everyday
language (we shall always say: to melt sugar in water) is certainly
not without foundation. Certain of the reasons which might be invoked
to uphold this opinion are too evident to be repeated here, though
others more recondite might be quoted. The fact that the internal
energy generally becomes independent of the concentration when the
dilution reaches even a moderately high value is rather in favour of
the hypothesis of fusion.

We must not forget, however, the continuity of the liquid and gaseous
states; and we may consider it in