by mm' Cf^-2. It is easy to show that a force subject to
this law would not account for capillary action. We shall, therefore,
in what follows, consider only that part of the force which depends on
[phi](f), where [phi](f) is a function of f which is insensible for
all sensible values of f, but which becomes sensible and even
enormously great when f is exceedingly small.

If we next introduce a new function of f and write
_
/ [oo]
| [phi](f)df = [Pi](f), (23)
_/f

then mm' [Pi](f) will represent--(1) The work done by the attractive
force on the particle m, while it is brought from an infinite distance
from m' to the distance f from m'; or (2) The attraction of a particle
m on a narrow straight rod resolved in the direction of the length of
the rod, one extremity of the rod being at a distance f from m, and
the other at an infinite distance, the mass of unit of length of the
rod being m'. The function [Pi](f) is also insensible for sensible
values of f, but for insensible values of f it may become sensible and
even very great.

If we next write
_
/ [oo]
| f[Pi](f)df = [psi](z), (24)
_/z

then 2[pi]m[sigma][psi](z) will represent--(1) The work done by the
attractive force while a particle m is brought from an infinite
distance to a distance z from an infinitely thin stratum of the
substance whose mass per unit of area is [sigma]; (2) The attraction
of a particle m placed at a distance z from the plane surface of an
infinite solid whose density is [sigma].

[Illustration: FIG. 2]

Let us examine the case in which the particle m is placed at a
distance z from a curved stratum of the substance, whose principal
radii of curvature are R1 and R2. Let P (fig. 2) be the particle and
PB a normal to the surface. Let the plane of the paper be a normal
section of the surface of the stratum at the point B, making an angle
[omega] with the section whose radius of curvature is R1. Then if O is
the centre of curvature in the plane of the paper, and BO = u,

1 cos^2[omega] sin^2[omega]
-- = ------------ + -----------. (25)
u R1 R2

Let POQ = [theta], PO = r, PQ = f, BP = z,

f^2 = u^2 + r^2 - 2ur cos[theta]. (26)

The element of the stratum at Q may be expressed by

[sigma]u^2 sin[theta] d[theta] d[omega],

or expressing d[Greek: th] in terms of