J. Trowbridge — Vortex Rings in Liquids. 331 



liquid slowly diffuses itself through another liquid of different 

 density. 

 By a consideration of the equatio 



given by Helmholtz, from which he draws the conclusion that 

 "each vortex line remains continually composed of the same 

 elements of fluid, and swims forward with" them in the fluid," 

 we see, on introducing the new expressions which we have 

 found for — , &c, Eq. (11), that we approach nearer and nearer 

 to this theoretical conclusion when the variations of h are 

 smaller and smaller. Obviously, we should then obtain the 

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

 motion takes place are composed of the same liquid. And, 

 therefore, a drop of water falling into water must form a more per- 

 fect ring than that formed by a drop of any colored liquid of greater 

 density than water. 



The formation of these liquid rings is as fascinating and as 

 simple an occupation as blowing soap-bubbles. All liquids 

 falling from such a height that the surface of the liquid is not 

 too much disturbed to enable the drop to be acted upon sym- 

 metrically by the forces at the free surface will form rings, if 

 too great differences of density do not exist, and if the drop can 

 diffuse in the liquid. The preceding mathematical discussion, 

 as we have seen, shows us that a drop of pure water on striking 

 the same element under the above conditions must necessarily 

 assume the ring shape. This can be shown experimentally by 

 covering the free surface of the water with a fine powder or 

 with matter in a fine state of subdivision. I have found that 

 an alcoholic tincture of ginger, which gives ©n the surface of 

 water a milky liquid consisting of particles in a fine state o 

 subdivision, answers the purpose very well. Fine particles will 

 be carried down by the jeen to rotate in a vor- 



tex ring far below the surface. This fact can be stated, also, by 

 the employment of any of the aniline colors which are solvent 

 in water, the falling i ! i Jowd solution, whose 



specific gravity does not differ sensibly from that of water. 1 be 

 method that I have employed to produce the rings consists 

 merely of a small glass tube, slightly smaller at one end than 

 the other. A bit of cotton is wedged in nearer the larger end 

 over which a piece of flexible rubber tubing is slipped. VV ltn 



