olumn, the volume of the suspended column is [pi]r^2h, and
its weight is [pi][rho]gr^2h, when [rho] is its density and g the
intensity of gravity. Equating this force with the resultant of the
tension

[pi][rho]gr^2h = 2[pi]rT cos[alpha],

or

h = 2T cos ([alpha]/[rho]gr).

Hence the mean height to which the fluid rises is inversely as the
radius of the tube. For water in a clean glass tube the angle of contact
is zero, and

h = 2T/[rho]gr.

For mercury in a glass tube the angle of contact is 128 deg. 52', the
cosine of which is negative. Hence when a glass tube is dipped into a
vessel of mercury, the mercury within the tube stands at a lower level
than outside it.

_Rise of a Liquid between Two Plates_.--When two parallel plates are
placed vertically in a liquid the liquid rises between them. If we now
suppose fig. 6 to represent a vertical section perpendicular to the
plates, we may calculate the rise of the liquid. Let l be the breadth of
the plates measured perpendicularly to the plane of the paper, then the
length of the line which bounds the wet and the dry parts of the plates
inside is l for each surface, and on this the tension T acts at an angle
[alpha] to the vertical. Hence the resultant of the surface-tension is
2lT cos[alpha]. If the distance between the inner surfaces of the plates
is a, and if the mean height of the film of fluid which rises between
them is h, the weight of fluid raised is [rho]ghla. Equating the
forces--

[rho]ghla = 2lT cos[alpha],

whence

h = 2T cos ([alpha]/[rho]ga).

This expression is the same as that for the rise of a liquid in a tube,
except that instead of r, the radius of the tube, we have a the distance
of the plates.

_Form of the Capillary Surface_.--The form of the surface of a liquid
acted on by gravity is easily determined if we assume that near the part
considered the line of contact of the surface of the liquid with that of
the solid bounding it is straight and horizontal, as it is when the
solids which constrain the liquid are bounded by surfaces formed by
horizontal and parallel generating lines. This will be the case, for
instance, near a flat plate dipped into the liquid. If we suppose these
generating lines to be normal to the plane of the paper, then all
sections of the solids parallel to this plane will be equal and similar
to each other, and the section of the surface of the liquid will be of
the same form for all such sections.

[I