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Mr. C. A. Bell. 



[May 13, 



however complex their form. For this growth takes place inde- 

 pendently of the "forces of figure," and under conditions 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 properties 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 

 motions of the stream may be regarded as resultants of the motions 

 of an infinite series of parallel and coaxial 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 circular. In a frictionless fluid a vortex-ring, uninfluenced 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 equalise the velocities. At a distance from the orifice, 

 therefore, depending 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 plays 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 be 

 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 com- 

 municated to the fluid, either behind or external to the orifice, or to 

 the orifice itself, must alter the vorticity of the stream. That vortex- 

 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 



