, travelling over the surface. If v =
[lambda]/[tau] we have

[rho][lambda]^3 2[pi]h g[lambda]^2[rho]
T = --------------- - coth-------- - ---------------- (2)
2[pi][tau]^2 [lambda] 4[pi]^2

h denoting the depth of the liquid. In observations upon ripples the
factor involving h may usually be omitted, and thus in the case of water
([rho] = 1)

[lambda]^3 g[lambda]^2
T = ------------ - ------------ (3)
2[pi][tau]^2 4[pi]^2

simply. The method has the advantage of independence of what may occur
at places where the liquid is in contact with solid bodies.

The waves may be generated by electrically maintained tuning-forks from
which dippers touch the surface; but special arrangements are needed for
rendering them visible. The obstacles are (1) the smallness of the
waves, and (2) the changes which occur at speeds too rapid for the eye
to follow. The second obstacle is surmounted by the aid of the
stroboscopic method of observation, the light being intermittent in the
period of vibration, so that practically only one phase is seen. In
order to render visible the small waves employed, and which we may
regard as deviations of a plane surface from its true figure, the
method by which Foucault tested reflectors is suitable. The following
results have been obtained

Clean 74.0
Greasy to the point where camphor motions nearly cease 53.0
Saturated with olive oil 41.0
Saturated with sodium oleate 25.0

(_Phil. Mag._ November 1890) for the tensions of various water-surfaces
at 18 deg. C., reckoned in C.G.S. measure.

The tension for clean water thus found is considerably lower than that
(81) adopted by Quincke, but it seems to be entitled to confidence, and
at any rate the deficiency is not due to contamination of the surface.

A calculation analogous to that of Lord Kelvin may be applied to find
the frequency of small transverse vibrations of a cylinder of liquid
under the action of the capillary force. Taking the case where the
motion is strictly in two dimensions, we may write as the polar equation
of the surface at time t

r = a + a_n cos n[theta] cos pt, (4)

where p is given by

T
p^2 = (n^3 - n)--------. (5)
[rho]a^3

If n = 1, the section remains circular, there is no force