104 Proceedings of the Royal Society 
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 trans- 
formations 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 dimen- 
sions 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 momentum 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 full theory of the swelling of 
vortex atoms by elevation 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 
six or eight inches diameter cut in the opposite side. A common 
rough packing-box of two 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 retorts 
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 interesting 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- 
