m. Thus

____
\/(2gh)
frequency = ------- (4)
4.508d

But the most certain method of obtaining complete regularity of
resolution is to bring the reservoir under the influence of an external
vibrator, whose pitch is approximately the same as that proper to the
jet. H.G. Magnus (_Pogg. Ann._ cvi., 1859) employed a Neef's hammer,
attached to the wooden frame which supported the reservoir. Perhaps an
electrically maintained tuning-fork is still better. Magnus showed that
the most important part of the effect is due to the forced vibration of
that side of the vessel which contains the orifice, and that but little
of it is propagated through the air. With respect to the limits of
pitch, Savart found that the note might be a fifth above, and more than
an octave below, that proper to the jet. According to theory, there
would be no well-defined lower limit; on the other side, the external
vibration cannot be efficient if it tends to produce divisions whose
length is less than the circumference of the jet. This would give for
the interval defining the upper limit [pi] : 4.508, which is very nearly
a fifth. In the case of Plateau's numbers ([pi] : 4.38) the discrepancy
is a little greater.

The detached masses into which a jet is resolved do not at once assume
and retain a spherical form, but execute a series of vibrations, being
alternately compressed and elongated in the direction of the axis of
symmetry. When the resolution is effected in a perfectly periodic
manner, each drop is in the same phase of its vibration as it passes
through a given point of space; and thence arises the remarkable
appearance of alternate swellings and contractions described by Savart.
The interval from one swelling to the next is the space described by the
drop during one complete vibration, and is therefore (as Plateau shows)
proportional _ceteris paribus_ to the square root of the head.

The time of vibration is of course itself a function of the nature of
the fluid and of the size of the drop. By the method of dimensions alone
it may be seen that the time of infinitely small vibrations varies
directly as the square root of the mass of the sphere and inversely as
the square root of the capillary tension; and it may be proved that its
expression is

/ / 3[pi][rho]V \
r = / ( ----------- ), (5)
\/ \ 8T /

V being the volume of the vibrating mass.

In cons