24 Sir William Thomson on Vortex Atoms, 



holtz/s investigation proves that the angular vortex velocity of 

 the core varies directly as its length, or inversely as its sectional 

 area. Hence the strength of the electric current in the electro- 

 magnet, corresponding to an infinitely thin vortex core, remains 

 constant, however much its length may be altered in the course 

 of the transformations which it experiences by the motion of 

 the fluid. Hence it is obvious that the larger the diameter of 

 the ring for the same volume and strength of vortex motions 

 in an ordinary Helmholtz ring, the greater is the whole kinetic 

 energy of the fluid, and the greater is the momentum ; and 

 we therefore see that the dimensions of a Helmholtz ring are 

 determinate when the volume and strength of the vortex motion 

 are given, and, besides, either the kinetic energy or the momen- 

 tum of the whole fluid motion due to it. Hence if, after any 

 number of collisions or influences, a Helmholtz ring escapes to 

 a great distance from others and is then free, or nearly free, from 

 vibrations, its diameter will have been increased or diminished 

 according as it has taken energy from, or given energy to, the 

 others. A fall theory of the swelling of vortex atoms by eleva- 

 tion of temperature is to be worked out from this principle. 



Professor Tait's plan of exhibiting smoke-rings is as follows : — 

 A large rectangular box, open at one side, has a circular hole 

 of 6 or 8 inches diameter cut in the opposite side. A common 

 rough packing-box of 2 feet cube, or thereabout, will answer the 

 purpose very well. The open side of the box is closed by a stout 

 towel or piece of cloth, or by a sheet of india-rubber stretched 

 across it. A blow on this flexible side causes a circular vortex 

 ring to shoot out from the hole on the other side. The vortex 

 rings thus generated are visible if the box is filled with smoke. 

 One of the most convenient ways of doing this is to use two re- 

 torts with their necks thrust into holes made for the purpose in 

 one of the sides of the box. A small quantity of muriatic acid 

 is put into one of these retorts, and of strong liquid ammonia 

 into the other. By a spirit-lamp applied from time to time to 

 one or other of these retorts, a thick cloud of sal-ammoniac is 

 readily maintained in the inside of the box. A curious and in- 

 teresting experiment may be made with two boxes thus arranged, 

 and placed either side by side close to one another or facing one 

 another so as to project smoke-rings meeting from opposite direc- 

 tions — or in various relative positions, so as to give smoke-rings 

 proceeding in paths inclined to one another at any angle, and pass- 

 ing one another at various distances. An interesting variation of 

 the experiment may be made by using clear air without smoke 

 in one of the boxes. The invisible vortex rings projected from 

 it render their existence startlingly sensible when they come near 

 any of the smoke-rings proceeding from the other box. 



