t if C had been placed in any other position than the middle,
its equilibrium would have been stable. Hence the film is stable as
regards longitudinal displacements. It is also stable as regards
displacements transverse to the axis, for the film is in a state of
tension, and any lateral displacement of its middle parts would produce
a resultant force tending to restore the film to its original position.
Hence if the length of the cylindric film is less than its
circumference, it is in stable equilibrium. But if the length of the
cylindric film is greater than its circumference, and if we suppose the
disk C to be placed midway between A and B, and to be moved towards A,
the pressure on the side next A will diminish, and that on the side next
B will increase, so that the resultant force will tend to increase the
displacement, and the equilibrium of the disk C is therefore unstable.
Hence the equilibrium of a cylindric film whose length is greater than
its circumference is unstable. Such a film, if ever so little disturbed,
will begin to contract at one secton and to expand at another, till its
form ceases to resemble a cylinder, if it does not break up into two
parts which become ultimately portions of spheres.

_Instability of a Jet of Liquid._--When a liquid flows out of a vessel
through a circular opening in the bottom of the vessel, the form of the
stream is at first nearly cylindrical though its diameter gradually
diminishes from the orifice downwards on account of the increasing
velocity of the liquid. But the liquid after it leaves the vessel is
subject to no forces except gravity, the pressure of the air, and its
own surface-tension. Of these gravity has no effect on the form of the
stream except in drawing asunder its parts in a vertical direction,
because the lower parts are moving faster than the upper parts. The
resistance of the air produces little disturbance until the velocity
becomes very great. But the surface-tension, acting on a cylindric
column of liquid whose length exceeds the limit of stability, begins to
produce enlargements and contractions in the stream as soon as the
liquid has left the orifice, and these inequalities in the figure of the
column go on increasing till it is broken up into elongated fragments.
These fragments as they are falling through the air continue to be acted
on by surface-tension. They therefore shorten themselves, and after a
series of oscillations in which they become alte