502 



SCIENCE. 



[Vol. VII., No. 174 



and its greater sensitiveness to particular tones 

 may thereby be explained, Plateau's theory cannot 

 be held to account for the uniform growth, along 

 the jet- path, of all changes, however complex 

 their form ; for this growth takes place indepen- 

 dently of the ' forces of figure,' and under condi- 

 tions in which they are entirely absent, as when a 

 gaseous or liquid jet plays within a mass of fluid 

 of its own kind. 



The author is inclined, rather, to refer the prop- 

 erties of jets of all kinds to conditions of motion 

 on which hitherto little stress has been laid ; viz., 

 the unequal velocities at different points in the 

 stream after it has left the orifice. From the axis 

 towards the circumference of a jet near the orifice, 

 the velocity diminishes continuously, and the mo- 

 tions of the stream may be regarded as resultants 

 of the motions of an infinite series of parallel and 

 co-axial vortex-rings. In many respects, in fact, 

 the appearance of a jet resembles the appearance 

 of a vortex-ring projected from the same orifice. 

 Thus a jet from a circular orifice, like a vortex- 

 ring from a round aperture, remains always circu- 

 lar. In a frictionless fluid a vortex-ring, uninflu- 

 enced by other vortices, would remain of constant 

 diameter, — a condition to which a horizontal 

 liquid jet approximates. When, however, the 

 ring moves through a viscous fluid, it experiences 

 retardation and expansion, which are precisely 

 the changes which a jet playing in a fluid of its 

 own kind undergoes. The vibrating smoke-ring 

 projected from an elliptical aperture changes its 

 form in exactly the same manner as a jet, at 

 sufficiently low pressure, from an elliptical 

 orifice. These analogies might be considerably 

 extended. 



In a liquid jet in air or in a vacuum, internal 

 friction must gradually equalize the velocities. 

 At a distance from the orifice, therefore, depend- 

 ing on the viscosity of the liquid, such a jet must 

 approach the condition of a cylinder at rest, and 

 must tend to divide in accordance with Plateau's 

 law. The rapidity with which drops are formed 

 depends mainly on the superficial tension of the 

 liquid. The length of the continuous column 

 should therefore bear some inverse ratio to the 

 viscosity and superficial tension of the liquid, — a 

 view which is in harmony with the results of 

 Savart's experiments, and some of the author's, in 

 this direction. 



Where the jet pla\s into a fluid of its own kind, 

 the retardation and expansion which it experiences 

 are mainly due to its parting with its energy to 

 the surrounding medium. When, as a result of 

 vibration, growing swellings and contractions are 

 formed in it, this loss must he more rapid : and 

 the jet therefore shows a diminution of mean 



velocity along the axis, which increases with the 

 distance from the orifice. 



Such being the conditions, it is evident that any 

 impulse communicated to the fluid, either behind 

 or external to the orifice, or to the orifice itself, 

 must alter the vorticity of the stream. That vor- 

 tex-rings are generated by impulses of the first 

 kind is well known ; the action when the orifice 

 is moved is intelligible, if we consider that a 

 forward motion of it will produce acceleration, a 

 backward motion retardation, of the outer layers 

 of the jet. As the result of a rapid to-and-fro 

 motion, we may then imagine two vortex-rings to 

 be developed ; the foremost layer of greater 

 energy, and moving more slowly, than the hind- 

 most. These two rings, in their onward course, 

 will then act on each other in a known manner : 

 the first will grow in size and energy at the expense 

 of the second, at the same time diminishing in 

 velocity ; the second will contract while its velocity 

 increases. The inequalities in cross-section, initi- 

 ated at the orifice, thus tend to grow along the 

 jet-path, and will be attended also by growing in- 

 equalities of the normal and rotational velocities 

 of the particles. Since the stream-lines of a 

 vortex-ring are crowded together at its centre, the 

 disturbances produced by impact of the jet-rings 

 will be greatest along the axis, and least along the 

 circumference. 



Indeed, the sound disturbances produced by im- 

 pact of a common vortex-ring are quite analogous 

 to those of a vibrating jet. Let an air-ring be 

 projected into a trumpet-shaped tube connected 

 with the ear, and little more than a rushing noise 

 will result ; but let it be projected against a small 

 orifice in the hearing tube, and a sharp click will 

 be heard at the moment of impact. This click is 

 loud when the centre of the ring strikes the tube, 

 but faint, although still of the same character, 

 when produced from the circumference. 



The foregoing considerations may be extended 

 to cases in which the motions of the orifice are 

 complex vibrations. Expansions and contractions 

 are then initiated in the fluid proportional at every 

 point to the velocity of the orifice. The inequali- 

 ties must tend to further diverge in the manner 

 described. 



Similar considerations apply to cases in which 

 the motions of the orifice are the result of lateral 

 impulses. In these cases the rings formed in the 

 jet will not be perpendicular to its direction, and 

 in their onward course may possibly vibrate about 

 a mean position. 



The author further pointed out how the viscosity 

 and surface-tension of the fluid may influence its 

 sensitiveness. When the surface-tension is very 

 high, as in mercury, it produces a tendency in the 



