10 M. J. Plateau on Jets of Liquid under the 
hence the duration of each of the vibrations in question, like that 
of the passage of a contraction or an expansion, is equal to half 
the time of passage of a division, and we may thus deduce the 
following fundamental conclusion :— 
The duration of each of the vibrations corresponding to the note 
produced by a jet is equal to that of the passage of a contraction 
or an expansion at the contracted section. 
§ 5. Let us now suppose, that, by means of the expedients in- 
dicated by Savart, the jet is first protected from the influence of 
vibrations proceeding from the fall of the liquid into the receiving 
vessel and from external noises, and then—the jet being thus 
abandoned to the sole action of the forces of figure—-that a note 
exactly in unison with that which would be produced by the 
shock of the discontinuous part against a stretched membrane, 
is transmitted to the vessel whence the jet issues, and thus to the 
liquid it contains. The liquid is in a state of vibration as it 
flows from the interior of the vessel towards the orifice ; conse- 
quently, if these vibrations have a vertical direction, each portion 
of the jet which passes the contracted section during the execu- 
tion of a descending vibration will be animated with the velocity 
V 2h, together with that of this vibration, and hence such a 
portion will contain more liquid than that which would have 
passed during the same time in the absence of these vibrations. 
The excess of velocity will, in fact, tend to communicate itself to 
the part of the jet situated below that which we are now consi- 
dering ; but, disregarding for a moment the action of the forces 
of figure, we must at least admit that this inferior part will, by 
its inertia, offer a certain resistance ; and that, as a consequence, 
the excess of liquid brought by the excess of velocity will tend to 
spread itself out horizontally, or, in other words, to produce a 
lateral expansion of the portion of the jet to which it belongs. 
This granted, if the figure (almost cylindrical) which the jet 
would assume by the sole effects of the translatory motion of the 
liquid and of the circular form of the orifice were a figure of 
stable equilibrium, the portion which, under the action of the 
descending vibration, expands laterally as it passes the contracted 
section, would at the same time strive to regain its former shape. 
It follows from this, under the hypothesis in question, that as 
the expansion developed itself, it would also propagate itself to 
the underlying strata, and would constitute upon the surface of 
the jet an elevated wave of a certain length, which would descend 
with a velocity equal to the sum of that of its propagation and 
that of the liquid. Again, the portion of the jet which would 
immediately afterwards pass the contracted section in an ascend- 
ing phase of vibration, and which on that account would tra- 
verse the same with the velocity 2gA diminished by that of 
