expect considerable
variation of density, even when we take into account the smallness of
the compressibility of liquids.

The pressure at any point of the liquid arises from two causes, the
external pressure P to which the liquid is subjected, and the pressure
arising from the mutual attraction of its molecules. If we suppose
that the number of molecules within the range of the attraction of a
given molecule is very large, the part of the pressure arising from
attraction will be proportional to the square of the number of
molecules in unit of volume, that is, to the square of the density.
Hence we may write

p = P + A[rho]^2,

where A is a constant [equal to Laplace's intrinsic pressure K. But
this equation is applicable only at points in the interior, where
[rho] is not varying.]

[The intrinsic pressure and the surface-tension of a uniform mass are
perhaps more easily found by the following process. The former can be
found at once by calculating the mutual attraction of the parts of a
large mass which lie on opposite sides of an imaginary plane
interface. If the density be [sigma], the attraction between the whole
of one side and a layer upon the other distant z from the plane and of
thickness dz is 2[pi][sigma]^2[psi](z)dz, reckoned per unit of area.
The expression for the intrinsic pressure is thus simply
_
/ [oo]
K = 2[pi][sigma]^2 | [psi](z)dz. (28)
_/0

In Laplace's investigation [sigma] is supposed to be unity. We may
call the value which (28) then assumes K0, so that as above
_
/ [oo]
K0 = 2[pi] | [psi](z)dz. (29)
_/0

The expression for the superficial tension is most readily found with
the aid of the idea of superficial energy, introduced into the subject
by Gauss. Since the tension is constant, the work that must be done to
extend the surface by one unit of area measures the tension, and the
work required for the generation of any surface is the product of the
tension and the area. From this consideration we may derive Laplace's
expression, as has been done by Dupre (_Theorie mecanique de la
chaleur_, Paris, 1869), and Kelvin ("Capillary Attraction," _Proc.
Roy. Inst._, January 1886. Reprinted, _Popular Lectures and
Addresses_, 1889). For imagine a small cavity to be formed in the
interior