rnately elongated and
flattened, settle down into the form of spherical drops.

This process, which we have followed as it takes place on an individual
portion of the falling liquid, goes through its several phases at
different distances from the orifice, so that if we examine different
portions of the stream as it descends, we shall find next the orifice
the unbroken column, then a series of contractions and enlargements,
then elongated drops, then flattened drops, and so on till the drops
become spherical.

[The circumstances attending the resolution of a cylindrical jet into
drops were admirably examined and described by F. Savart ("Memoire sur
la constitution des veines liquides lancees par des orifices circulaires
en minces parois," _Ann. d. Chim._ t. liii., 1833) and for the most part
explained with great sagacity by Plateau. Let us conceive an infinitely
long circular cylinder of liquid, at rest (a motion common to every part
of the fluid is necessarily without influence upon the stability, and
may therefore be left out of account for convenience of conception and
expression), and inquire under what circumstances it is stable or
unstable, for small displacements, symmetrical about the axis of figure.

Whatever the deformation of the originally straight boundary of the
axial section may be, it can be resolved by Fourier's theorem into
deformations of the harmonic type. These component deformations are in
general infinite in number, of very wave-length and of arbitrary phase;
but in the first stages of the motion, with which alone we are at
present concerned, each produces its effect independently of every
other, and may be considered by itself. Suppose, therefore, that the
equation of the boundary is

r = a + a cos kz, (1)

where a is a small quantity, the axis of z being that of symmetry. The
wave-length of the disturbance may be called [lambda], and is connected
with k by the equation k =2[pi]/[lambda]. The capillary tension
endeavours to contract the surface of the fluid; so that the stability,
or instability, of the cylindrical form of equilibrium depends upon
whether the surface (enclosing a given volume) be greater or less
respectively after the displacement than before. It has been proved by
Plateau (_vide supra_) that the surface is greater than before
displacement if ka > 1, that is, if [lambda] < 2[pi]a; but less if ka <
1, or [lambda] > 2[pi]a. Accordingly, the equilibrium is stable if
[lamb