tion. With its sign reversed it is now called
the potential energy of the system. It consists of three parts, the
first depending on the action of gravity, the second on the mutual
action between the particles of the fluid, and the third on the action
between the particles of the fluid and the particles of a solid or fluid
in contact with it.

The condition of equilibrium is that this expression (which we may for
the sake of distinctness call the potential energy) shall be a minimum.
This condition when worked out gives not only the equation of the free
surface in the form already established by Laplace, but the conditions
of the angle of contact of this surface with the surface of a solid.

Gauss thus supplied the principal defect in the great work of Laplace.
He also pointed out more distinctly the nature of the assumptions which
we must make with respect to the law of action of the particles in order
to be consistent with observed phenomena. He did not, however, enter
into the explanation of particular phenomena, as this had been done
already by Laplace, but he pointed out to physicists the advantages of
the method of Segner and Gay Lussac, afterwards carried out by Quincke,
of measuring the dimensions of large drops of mercury on a horizontal or
slightly concave surface, and those of large bubbles of air in
transparent liquids resting against the under side of a horizontal plate
of a substance wetted by the liquid.

In 1831 Simeon Denis Poisson published his _Nouvelle Theorie de l'action
capillaire_. He maintained that there is a rapid variation of density
near the surface of a liquid, and he gave very strong reasons, which
have been only strengthened by subsequent discoveries, for believing
that this is the case. He proceeded to an investigation of the
equilibrium of a fluid on the hypothesis of uniform density, and arrived
at the conclusion that on this hypothesis none of the observed capillary
phenomena would take place, and that, therefore, Laplace's theory, in
which the density is supposed uniform, is not only insufficient but
erroneous. In particular he maintained that the constant pressure K,
which occurs in Laplace's theory, and which on that theory is very
large, must be in point of fact very small, but the equation of
equilibrium from which he concluded this is itself defective. Laplace
assumed that the liquid has uniform density, and that the attraction of
its molecules extends to a finite though insens