MR. C. A. BELL OK THE SYMPATHETIC VIBRATIONS OF JETS. 
419 
loses energy by setting up rotatory or other motions in the surrounding medium. The 
rate of this loss depends on the velocity of the jet; and since the outer layers are 
most retarded, it is attended by increased vorticity. Now, at very low pressures, the 
fall in velocity from the axis outward is not steep, and the jet, therefore, travels as a 
nearly uniform stream to a considerable distance. Up to a certain point the length 
of the continuous stream increases with the pressure ; and where discontinuity occurs 
the jet appears to dissipate rather than to break up in any regular manner. The con¬ 
tinuous column of a smoke jet in air may thus extend to 12 inches, and of a coloured 
water jet in water to 4 or 5 inches, when the orifice is from 1 to \\ mm. in diameter. 
If the jet in this condition be disturbed by a gentle tap on the supports, a break 
appears close to the orifice, and behind the break a portion of the fluid appears to 
be thrown off from the main stream. In the mass thus detached distinct rotatory 
motions may be seen similar to those observed in a smoke ring when it has nearly 
reached the end of its career, and is almost stationary. 
The production of vortex rings by interrupting the flow of a water jet in water, has 
already been noticed by Oberbeck.* 
When the pressure is increased to a point at which the jet answers to tones of high 
pitch, the appearance changes. The nearly cylindrical part becomes much shorter, 
and beyond this the jet expands rapidly in the form of an aigrette, or divergent 
brush. The motion may then be compared to that of a smoke ring which travels with 
nearly uniform diameter for a certain distance, but which expands rapidly when its 
velocity has been considerably reduced by the surrounding air. 
I have mentioned above that when a vibrating jet of air is directed into the 
trumpet-shaped end of a hearing-tube, its vibrations are almost quite inaudible ; but 
that relatively loud sounds are produced when the hearing orifice is very small and 
placed in the jet axis. A phenomenon strictly parallel to this may be noticed with 
vortex rings in air. Let a ring, for convenience rendered visible by smoke, be 
projected into a large funnel connected by a tube with the ear, and the only sound 
resulting from its impact within the funnel will be a kind of rushing noise. But let 
it be projected against a small orifice in the end of the hearing-tube, and a sharp 
click will be heard when the ring strikes the orifice. This click will be loudest when 
produced from the centre of the ring, and faintest, although still sharp and clear, 
when produced from its circumference. The analogy is thus complete. These effects 
may be obtained from the ring so long as it continues to move. 
Now, assuming that a jet is composed of an infinite number of circular vortex 
filaments, vibrations impressed upon the orifice may be supposed to act somewhat 
in the following way. The vorticity of the jet, as we have seen, is the result of 
the unequal velocities of the layers composing it. Any disturbance, therefore, which 
alters the rate or distribution of velocities at the orifice, must also change the 
vorticity of the jet. To take a simple case, let the vibratory motions of the orifice 
* Anna! Phys. Chem., ser. 2, vol. 2, pp. 1-17. 
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