of
restitution, and p = 0. The principal vibration, in which the section
becomes elliptical, corresponds to n = 2.

Vibrations of this kind are observed whenever liquid issues from an
elliptical or other non-circular hole, or even when it is poured from
the lip of an ordinary jug; and they are superposed upon the general
progressive motion. Since the phase of vibration depends upon the time
elapsed, it is always the same at the same point in space, and thus the
motion is _steady_ in the hydrodynamical sense, and the boundary of the
jet is a fixed surface. In so far as the vibrations may be regarded as
isochronous, the distance between consecutive corresponding points of
the recurrent figure, or, as it may be called, the _wave-length_ of the
figure, is directly proportional to the velocity of the jet, i.e. to the
square root of the head. But as the head increases, so do the _lateral_
velocities which go to form the transverse vibrations. A departure from
the law of isochronism may then be expected to develop itself.

The transverse vibrations of non-circular jets allow us to solve a
problem which at first sight would appear to be of great difficulty.
According to Marangoni the diminished surface-tension of soapy water is
due to the formation of a film. The formation cannot be instantaneous,
and if we could measure the tension of a surface not more than 1/100 of
a second old, we might expect to find it undisturbed, or nearly so, from
that proper to pure water. In order to carry out the experiment the jet
is caused to issue from an elliptical orifice in a thin plate, about 2
mm. by 1 mm., under a head of 15 cm. A comparison under similar
circumstances shows that there is hardly any difference in the
wave-lengths of the patterns obtained with pure and with soapy water,
from which we conclude that at this initial stage, the surface-tensions
are the same. As early as 1869 Dupre had arrived at a similar conclusion
from experiments upon the vertical rise of fine jets.

A formula, similar to (5), may be given for the frequencies of vibration
of a spherical mass of liquid under capillary force. If, as before, the
frequency be p/2[Pi], and a the radius of the sphere, we have

T
p^2 = n(n - 1)(n + 2)--------, (6)
[rho]a^3

n denoting the order of the spherical harmonic by which the deviation
from a spherical figure is expressed. To find the radius of the sphere
of water