MR. C. A. BELL ON THE SYMPATHETIC VIBRATIONS OF JETS. 
415 
analogy, therefore, is incomplete ; and, moreover, does not take into account the peculiar 
changes in the motion of the jet fluid. 
So peculiar are these changes, that the term “ vibration ” as applied to them seems 
to me entirely misleading. By this term is, commonly at least, signified a kind of 
motion, in which each particle of the vibrating body executes oscillations about a 
mean position, whether of rest or of steady motion, to which it tends to return when 
its motion is interfered with. But in a sounding jet the motions are not of this kind. 
Any vibration impressed on the orifice, produces a disturbance which tends to grow 
always in a definite direction ; and when the motions are interfered with, the particles 
do not return to their original positions. 
Plateau * on the other hand referred the normal vibrations of a jet to quite a 
different origin. Regarding the jet as a stationary cylinder of liquid, he proved 
experimentally that under the influence of the “forces of figure” alone, it would 
break up into shorter cylinders, the length and diameter of which would bear to each 
other a constant ratio. Each cylinder would further tend to assume a spherical form, 
by diminishing in length and increasing in diameter. Such changes must necessarily 
be attended by growing constrictions between successive cylinders ; and, finally, 
disruption must occur at these points, a succession of drops being detached from the 
stream. At the moment of its liberation, each drop would be in a state of tension 
or elongation, and thereafter would execute oscillations about its form of stable 
equilibrium—the sphere. These oscillations always reaching the same phase at a 
definite distance from the orifice, would give rise to the appearance of the “ventres'” 
or swellings, noticed by Savart in the discontinuous part of a liquid jet. The 
tendency to divide would of course exist in the liquid cylinder from the moment of 
its formation ; but when the impulses due to the impact of the successive drops upon 
an obstacle are conveyed back to the orifice, they materially assist this tendency, and 
the stream consequently resolves itself into drops nearer to the orifice. 
The normal vibrations of a liquid jet are thus completely and satisfactorily accounted 
for; and Plateau by an ingenious train of reasoning, showed also that division 
might even occur at other than the normal points, thus explaining Savart’s 
observation, that a jet could vibrate under the influence of tones about one-fifth 
higher, and an octave lower, than its normal. Moreover, Lord Rayleigh in a later 
paper t has pointed out that theoretically the lower limit of effective tones is not well 
defined, thus bringing Plateau’s theory into closer agreement with the facts 
described in this paper. 
Now, while it is impossible to deny to this theory the merits of simplicity, of firm 
experimental foundation, and of being in harmony with facts previously known, there 
are, I think, cogent reasons why it cannot be held to account for the new phenomena 
described above. In the first place it is a fact of experience, already noticed by 
* Phil. Mag. ser. 4, vol. 12 (1856), p. 286, and vol. 14 (1857), pp. 1 and 431. 
| Proc. Roy. Soc., vol. 29 (1879), p. 71, and vol. 34 (1882), p. 130. 
