ular constitution of bodies it is
necessary to study the effect of forces which are sensible only at
insensible distances; and Laplace has furnished us with an example of
the method of this study which has never been surpassed. Laplace
investigated the force acting on the fluid contained in an infinitely
slender canal normal to the surface of the fluid arising from the
attraction of the parts of the fluid outside the canal. He thus found
for the pressure at a point in the interior of the fluid an expression
of the form

p = K + 1/2H(1/R + 1/R')

where K is a constant pressure, probably very large, which, however,
does not influence capillary phenomena, and therefore cannot be
determined from observation of such phenomena; H is another constant on
which all capillary phenomena depend; and R and R' are the radii of
curvature of any two normal sections of the surface at right angles to
each other.

In the first part of our own investigation we shall adhere to the
symbols used by Laplace, as we shall find that an accurate knowledge of
the physical interpretation of these symbols is necessary for the
further investigation of the subject. In the _Supplement to the Theory
of Capillary Action_, Laplace deduced the equation of the surface of the
fluid from the condition that the resultant force on a particle at the
surface must be normal to the surface. His explanation, however, of the
rise of a liquid in a tube is based on the _assumption_ of the constancy
of the angle of contact for the same solid and fluid, and of this he has
nowhere given a satisfactory proof. In this supplement Laplace gave many
important applications of the theory, and compared the results with the
experiments of Louis Joseph Gay Lussac.

The next great step in the treatment of the subject was made by C.F.
Gauss (_Principia generalia Theoriae Figurae Fluidorum in statu
Aequilibrii_, Gottingen, 1830, or _Werke_, v. 29, Gottingen, 1867). The
principle which he adopted is that of virtual velocities, a principle
which under his hands was gradually transforming itself into what is now
known as the principle of the conservation of energy. Instead of
calculating the direction and magnitude of the resultant force on each
particle arising from the action of neighbouring particles, he formed a
single expression which is the aggregate of all the potentials arising
from the mutual action between pairs of particles. This expression has
been called the force-func