294 Prof. J. Trowbridge on Liquid Vortex-Rings. 



found for A J-j ^-, equations (11), that we approach nearer 



and nearer to this conclusion when the variations of h are 

 smaller and smaller. Obviously we should therefore obtain 

 the most perfect liquid rings when the drop and the liquid in 

 which the motion takes place are composed of the same liquid. 

 A drop of water falling into water must form a more perfect 

 ring than that formed by a drop of any coloured liquid of 

 greater density than water ; and every drop of water falling 

 into water from a height not too great must necessarily form 

 a vortex-ring. 



The formation of liquid rings is as fascinating and as simple 

 an occupation as blowing soap-bubbles. All liquid drops fall- 

 ing from such a height that the surface of the liquid in which 

 they are about to diffuse is not too much disturbed to enable 

 the drop to be acted upon symmetrically by the forces at the 

 free surface, will form rings if too great differences of density 

 do not exist. That a drop of pure water will descend through 

 the same liquid in a vortex ring can be shown experimentally 

 by covering the free surface of the water with a fine light 

 powder. Particles of the powder will be carried down by the 

 drop and will be seen to rotate in a ring-shape far below the 

 surface. This fact can be shown also by the employment of 

 any of the aniline colours which are solvent in water, the drop 

 consisting of a coloured solution whose density does not differ 

 sensibly from that of water. The method which I have em- 

 ployed to produce the rings consists merely of a small glass 

 tube, slightly smaller at one end than the other. A piece of 

 cotton is wedged in the tube ; and flexible rubber tubing is 

 attached to the larger end. With the aid of the mouth one 

 can fill this tube with liquid and eject it in drops at pleasure. 

 A modification of the same apparatus enables one to form the 

 rings beneath the surface of the liquid. With a bent tube one 

 can send the rings through a liquid in any desired direction. 

 By means of a three-way glass joint and a small india-rubber 

 bag, one can send by the same impulse two rings whose paths 

 make any desired angle with each other. By dropping a suit- 

 able liquid through a layer of oil superincumbent on water 

 and glycerine, one can study the rings formed by the sudden 

 bursting of the enveloping film of oil when the drop strikes 

 the layer of water and glycerine. A simple method of study- 

 ing the mutual behaviour of half vortex-rings is to illuminate, 

 by means of a gaslight, the bottom of a flat white porcelain 

 dish filled with water, and to observe the shadows on the bot- 

 tom of the dish of the half vortex-rings formed by the move- 

 ment of two spatula along the surface. It can be readily seen 



