418 
MR. C. A. BELL ON THE SYMPATHETIC VIBRATIONS OF JETS. 
indefinitely : in the actual jet two forces tend to their destruction, viz., internal 
friction, or the viscosity of the fluid, and friction against the surrounding medium. 
In liquid jets in air the first of these is mainly operative; but when the jet is 
surrounded by a fluid of its own kind, the second is most effective. 
In the first case (of a liquid jet in air) internal friction must bring about a gradual 
equalization of the velocities of the liquid particles, and at a distance from the orifice 
the jet will therefore approach the condition of a liquid cylinder at rest. As it does 
so it will gradually come under the operation of the “ forces of figure,” will divide, 
and ultimately resolve itself into drops. Owing to minute variations in the motions 
of the jet fluid the divisions will be somewhat irregular, but in the main they must 
tend to assume a rhythmical character, as pointed out by Plateau. 
The point at which discontinuity becomes apparent cannot, however, depend solely 
on the viscosity of the liquid, but must also depend on its superficial tension, which 
determines the rapidity of drop formation. If this theory is correct, it should be found 
then, that those liquids which are most mobile, and have the lowest surface tension, 
yield the longest continuous jets. Now experiments made by Savart have already 
shown this to be the case, although he connected the continuity of a jet with the 
compressibility of the liquid. Causing jets of ether, alcohol, and water to escape 
from a circular orifice 3 mms. in diameter, and under a pressure equal to 50 cms. of the 
liquid, he found the continuous columns to be 90, 85, and 70 cms. in length respec¬ 
tively. The compressibility of the liquids are to each other as 131'35 : 94'95 : 47‘85, 
in accordance with Savart’s theory. On the other hand, the coefficients of internal 
friction are '59213 ; P3754 and IT858 for these liquids respectively (Helmholtz and 
Pitrowski), and the superficial tensions in contact with air 1 '88, 2'5 and 7'3 milli¬ 
grams per millimetre. Savart’s observations are, therefore, equally in harmony with 
the theory here proposed. Thus, while water and alcohol do not differ widely in 
viscosity, drops are sooner detached from a jet of the former liquid since it has the 
greater superficial tension. 
Both superficial tension and viscosity diminish with rise of temperature ; we should, 
therefore, expect to find that, other conditions being equal, a jet of hot liquid pre¬ 
serves its continuity through a greater distance than a jet of the same liquid cold. 
This I have found to be the case. In one experiment the continuous part of a jet of 
distilled water at 10" C. was about 17 cms. in length ; but increased to about 20 cms. 
when the water was heated to 70° C. # 
When a gaseous or liquid jet plays within a mass of fluid of the same kind, and 
when accordingly “ forces of figure ” do not exist, the analogy to a system of smoke- 
rings in air is much more evident. The action of internal friction in equalizing the 
velocities at different points in any section is now insignificant ; but the jet rapidly 
* Lord Rayleigh (Pliil. Mag., ser. 5, vol. 17 (18S4), p. 192) lias already pointed out the remarkable 
influence of viscosity, modified by changes in temperature, on the “ flaring ” pressure and sensitiveness 
of a liquid jet in liquid. 
