MR. C. A. BELL ON THE SYMPATHETIC VIBRATIONS OF JETS. 
417 
similar to those seen in liquid jets, and that these changes grow along the jet-path. 
I have only been able so far to observe this drop-like appearance in jets at low pres¬ 
sure, and even then the outline is somewhat obscured by trails of smoke detached 
from the stream. I hope, however, to succeed in getting good photographs of jets at 
high velocities. The practical difficulties in the way can no doubt be overcome. 
It seems to me that the true key to an explanation of the vibratory phenomena of 
both liquid and gaseous jets is to be found in the fact that the velocity of the stream 
issuing from a circular orifice is not equal at all points, but diminishes from the centre, 
or jet axis, outwards. When the efflux takes place from a straight circular tube (and 
even such a jet is “ sensitive ”) this may be caused by adhesion of the fluid to the 
sides of the tube, or by friction; but when the jet issues from a hole in a thin plate it 
is no doubt chiefly due to the convergence of the stream lines towards the orifice. 
This will tend to cause retardation of the normal velocity of the outer layers of fluid: 
indeed at the orifice the outermost layer of a liquid must be in a state of absolute 
rest. The fall in velocity from the centre of the stream outwards must evidently be 
more steep in small jets than in large ones; and as I have pointed out, it is precisely 
the former which give the most accurate reproduction of impressed vibrations. 
The normal jet, then, as it leaves the orifice is composed of an infinite number of 
cylindrical streams, the velocity of each being uniform in any section of it, but 
varying in some inverse ratio with its diameter. We thus have in the jet the 
characteristics of the forward motion of a vortex ring; and the motions of a jet may 
be considered to be the resultants of the motions of an infinite number of parallel and 
coaxial vortex rings, moving forward with the same velocity. 
This comparison of the jet with a series of vortex rings is not entirely fanciful, for 
experiment shows that when a jet and a vortex ring are projected from similar orifices, 
the outline of the jet at successive points along its path shows precisely the same 
shapes that are successively assumed by the vortex ring. For example, all sections of 
a jet from a circular orifice are circular, provided that there is nothing to interfere 
with the free motion of the fluid behind the orifice. With the same proviso, the 
smoke ring from a circular aperture remains always circular. If a jet orifice be 
elliptical, and the pressure not too high, successive sections of the jet as we proceed 
from the orifice will be alternately circular and elliptical, and the major axes of suc¬ 
cessive ellipses will be at right angles to each other. Now these succeeding shapes 
also characterize the well known vibrations of a smoke ring projected from an elliptical 
aperture. These analogies might easily be multiplied. Again, if the aperture in a 
smoke ring box be an elongated rectangle, a suitable tap on the diaphragm will 
frequently cause the projected ring to break up into two divergent rings, thus 
imitating the division of a vibrating jet into two streams ; a phenomenon which, when 
occurring under the influence of sound vibrations, I believe to be invariably due to 
some irregularity at or behind the orifice. 
Now, in a perfect fluid the system of rings composing the jet would continue 
MDCCCLXXXVI. 3 H 
