otion the tube and vessel are separated, preferably by a downward
movement of the latter. The inverted tube, with its suspended water,
being held in a clamp, a beaker containing a few drops of ether is
brought up from below until the free surface of the water is in contact
with ether vapour. The lowering of tension, which follows the
condensation of the vapour, is then strikingly shown by the sudden
precipitation of the water.]

_Effect of Surface-tension on the Velocity of Waves._--When a series of
waves is propagated on the surface of a liquid, the surface-tension has
the effect of increasing the pressure at the crests of the waves and
diminishing it in the troughs. If the wave-length is [lambda], the
equation of the surface is

y = b sin 2[pi](x/[lambda]).

The pressure due to the surface tension T is

d^2y 4[pi]^2
p = - T ---- = ---------- Ty.
dx^2 [lambda]^2

This pressure must be added to the pressure due to gravity g [rho] y.
Hence the waves will be propagated as if the intensity of gravity had
been

4[pi]^2 T
f = g + ---------- -----
[lambda]^2 [rho]

instead of g. Now it is shown in hydrodynamics that the velocity of
propagation of waves in deep water is that acquired by a heavy body
falling through half the radius of the circle whose circumference is the
wave-length, or

f[lambda] g[lambda] 2[pi]T
v^2 = --------- = --------- + -------------. (1)
2[pi] 2[pi] [rho][lambda]

This velocity is a minimum when
______
/ T
[lambda] = 2 [pi] / ------,
\/ g[rho]

and the minimum value is
_______
4 / Tg
v = / 4 -----.
\/ [rho]

For waves whose length from crest to crest is greater than [lambda], the
principal force concerned in the motion is that of gravitation. For
waves whose length is less than [lambda] the principal force concerned
is that of surface-tension. Lord Kelvin proposed to distinguish the
latter kind of waves by the name of ripples.

When a small body is partly immersed in a liquid originally at rest, and
moves horizontally with constant velocity V, waves are propagated
through the liquid with various velocities according to their respective
wave-lengths. In front of the body the relative velocity of the fluid
and the body varies from V where the fluid is at rest, to zero at the
cutwater