that of the interior space will be
V - S[epsilon].

If we suppose a normal [nu] less than [epsilon] to be drawn from the
surface S into the liquid, we may divide the shell into elementary
shells whose thickness is d[nu], in each of which the density and
other properties of the liquid will be constant.

The volume of one of these shells will be Sd[nu]. Its mass will be
S[rho]d[nu]. The mass of the whole shell will therefore be
_
/ [epsilon]
S | [ro]d[nu],
_/0

and that of the interior part of the liquid (V - S[epsilon])[rho]0. We
thus find for the whole mass of the liquid
_
/ [epsilon]
M = V [rho]0 - S | ([rho]0 - [rho]) d[nu]. (2)
_/0

To find the potential energy we have to integrate
_ _ _
/ / /
E = | | | [chi][rho] dx dy dz (3)
_/_/_/

Substituting [chi][rho] for [rho] in the process we have just gone
through, we find
_
/ [epsilon]
E = V[chi]0[rho]0 - S | ([chi]0[rho]0 - [chi][rho]) d[nu]. (4)
_/0

Multiplying equation (2) by [chi]0, and subtracting it from (4),
_
/ [epsilon]
E - M[chi]0 = S | ([chi] - [chi]0) d[nu]. (5)
_/0

In this expression M and [chi]0 are both constant, so that the
variation of the right-hand side of the equation is the same as that
of the energy E, and expresses that part of the energy which depends
on the area of the bounding surface of the liquid. We may call this
the surface energy.

The symbol [chi] expresses the energy of unit of mass of the liquid at
a depth [nu] within the bounding surface. When the liquid is in
contact with a rare medium, such as its own vapour or any other gas,
[chi] is greater than [chi]0, and the surface energy is positive. By
the principle of the conservation of energy, any displacement of the
liquid by which its energy is diminished will tend to take place of
itself. Hence if the energy is the greater, the greater the area of
the exposed surface, the liquid will tend to move in such a way as to
diminish the area of the exposed surface, or, in other words, the
exposed surface will tend to diminish if it can do so consistently
with the other conditions. This tendency of the surf