136 PROCEEDINGS OF THE AMERICAN ACADEMY 



very well. Fine particles will be carried down by the drop, and will 

 be seen to rotate in a vortex ring far below the surface. This fact can 

 be stated, al^o, bj'- the employment of any of the aniline colors which 

 are solvent in water, the falling drop consisting of a colored solution 

 whose specific gravity does not differ sensibly from that of water. The 

 metiiod that 1 have emploj^ed to produce the rings consists merely of a 

 small glass tube, slightly smaller at one end than the otiier. A bit of 

 cotton is wedged in nearer the larger end, over wliich a piece of flexi- 

 ble rubber tubing is slipped. AVith the aid of the moutli, one can fill 

 this tube with licpiid and eject it in drops at pleasure. The same appa- 

 ratus enables us to form the rings beneath the surface of the liquid. 

 With a tube bent horizontally, one can send the rings through a liquid 

 in any desired direction ; and, by means of a three-way glass joint and 

 a small india-rubber bag, one can send forth, by the same impulse, two 

 rings whose paths make any desired angle with each other. By partly 

 immersing the glass tubes connected with the three-way tube in the 

 free surface of the liquid, and covering tiie surface of the water with 

 fine powder, one can study the mutual behavior of half-vortex rings. 

 A simpler method is to illuminate, by means of a gas-light, the bottom 

 of a flat, white porcelain dish filled with water, and to observe the 

 shadows of the half-vortex rings on the bottom of tlie dish formed by 

 the movement of two spatulse along the surfiice. It can be readily seen, 

 by this simple method, that a lialf-vortex ring moving near another in 

 a parallel path and with a less velocity tends to follow in the path of 

 the first ; and that two equal half-vortex rings moving in opposite 

 directions along the same path separate into two vortices which move 

 at right angles to the path of the original vortices. We can conclude, 

 also, from this general discussion, that, whenever a mass of vapor of 

 greater density than the surrounding air is suddenly formed in the 

 higiier regions of the atmosphere, it tends to descend through it in a 

 vortex ring. 



The results of the preceding discussion are as follows : — 



1. An an^dogy between the strain potential and the velocity poten- 

 tial is indicated. 



2. It is shown that the formation of liquid rings is a necessary result 

 of the fumlameutal equations of strains and those of hydrodynamics ; 

 and that tlu-y constitute a general and not a special phenomenon. A 

 drop of water falling into water from a suitable height must assume a 

 ring shape. 



3. Vortices can and do arise in certain processes of diffusion. 



4. Simple methods of studying vortex motion in liquids are given. 



