isturbance is multiplied 2.7 times
in about one-ninth of a second. If the disturbance be multiplied 1000
fold in time, t, qt = 3log_e 10 = 6.9, so that t = .79d^(3/2). For
example, if the diameter be one millimetre, the disturbance is
multiplied 1000 fold in about one-fortieth of a second. In view of these
estimates the rapid disintegration of a fine jet of water will not cause
surprise.

The relative importance of two harmonic disturbances depends upon their
initial magnitudes, and upon the rate at which they grow. When the
initial values are very small, the latter consideration is much the more
important; for, if the disturbances be represented by a1e^(q1t),
a2e^(q2t), in which q1 exceeds q2, their ratio is (a1/a2) e^{-(q1-q2)t};
and this ratio decreases without limit with the time, whatever be the
initial (finite) ratio [alpha]2:[alpha]1. If the initial disturbances
are small enough, that one is ultimately preponderant for which the
measure of instability is greatest. The smaller the causes by which the
original equilibrium is upset, the more will the cylindrical mass tend
to divide itself regularly into portions whose length is equal to 4.5
times the diameter. But a disturbance of less favourable wave-length
may gain the preponderance in case its magnitude be sufficient to
produce disintegration in a less time than that required by the other
disturbances present.

The application of these results to actual jets presents no great
difficulty. The disturbances by which equilibrium is upset are impressed
upon the fluid as it leaves the aperture, and the continuous portion of
the jet represents the distance travelled during the time necessary to
produce disintegration. Thus the length of the continuous portion
necessarily depends upon the character of the disturbances in respect of
amplitude and wave-length. It may be increased considerably, as F.
Savart showed, by a suitable isolation of the reservoir from tremors,
whether due to external sources or to the impact of the jet itself in
the vessel placed to receive it. Nevertheless it does not appear to be
possible to carry the prolongation very far. Whether the residuary
disturbances are of external origin, or are due to friction, or to some
peculiarity of the fluid motion within the reservoir, has not been
satisfactorily determined. On this point Plateau's explanations are not
very clear, and he sometimes expresses himself as if the time of
disintegration depended only