1886.] 



On the Sympathetic Vibrations of Jets. 



377 



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 hindmost. These two rings in their onward course 

 will then act on each other in a known manner; the first wi]lgrow 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, initiated at the orifice, 

 thus tend to grow along the jet-path, and will be attended also by 

 growing inequalities 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 circum- 

 ference. 



Indeed the sound disturbances produced by impact 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 load 

 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 inequalities 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 points 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 jet 

 to break easily under the influence of moderate impulses. 



The foregoing is little more than the outlines of a new theory of 

 jet-vibrations. The author hopes to supply in the future further 

 experimental evidence in support of it. 



