THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
797 
If the core of the vortex-atoin is not vacuous but consists as in ordinary vortices of 
spinning fluid, here devoid of rotational elasticity, the rotational kinetic energy 
of the vortex as distinguished from translational energy will be a possible source of 
the phenomena of mass ; but to possess such energy the medium must have some 
ultimate structure, for in an infinitely small homogeneous element of volume the 
ratio of the rotational to translational part of the kinetic energy would be infinitely 
small. Such a structure, confined to the cores of the vortices, need not be in con¬ 
tradiction with Maxwell’s principle that the constitution of a perfect fluid cannot 
be molecular. 
\j\dded June 14, 1894.] 
On Natural Magnets. 
106. Lord Kelvin"^' has pointed out that the forcive between a pair of rigid cores 
in a fluid, with circulatory irrotational motion through their apertures, is equal but 
opposite to the forcive between the corresponding steady electric currents as expressed 
hy the electrodynamic formulte. The reason of this difference lies in the circumstance 
that the connexions and continuity of the fluid system prevent the circulation round 
any core from varying, so long as that core is unbroken; while the constraints must 
he less complete in the electrodynamic problem, because the currents change their 
values by induction. These constant circulations are of the nature of the constant 
momenta belonging to cyclic motions of dynamical systems ; and it is known that 
when such constant momenta are introduced into the expression for the energy in 
place of the corresponding velocities, the type of the general dy)iamical equation 
is thereby altered.! Tire modification which the equation of Least Action must 
undergo under these circumstances has been investigated on a previous occasion.| 
In the case of fluid circulation, when the cores are so thin as to interpose no sensible 
obstacle to the flow, the sign of that part of the kinetic energy which involves the 
cyclic constant of the motion has merely to be changed; in other words this energy 
is for the purpose of the modified dynamical ecjuations to be treated as potential 
instead of kinetic. In all cases in which co-ordinates of a dynamical system can be 
Ignored by elimination in this manner the energy function consists of two parts, 
one a quadratic function of the velocities of the bodies, the other a quadratic function 
of the constant momenta : in the case just mentioned the former part is negligible, so 
that the part whose sign is to be changed is practically the total energy. 
* Lord Kelvin (Sir W. Thomson), “ Hydrokiiietic Analogy,” ‘ Proc Roy. Soc., Edin.,’ 1870; ‘Papers 
on Electrostatics and Magnetism,’ p. .172. Also Kirchuoi'f, ‘ Crelle,’ 1869. 
t Routh, “Stability of Motion,” 1877, cb. 4, §§ 20 seq.; Thomson and Tait, “Natural Pbilosopby,” 
ed. 2, 1879, §§ 319, 320 ; von Helmholtz, “ On Polycyclic Systems,” ‘ Crelle,’ 1884-1887. 
X “ Least Action,” ‘ Proc. Lond. Matin Soc.,’ XV., March 1884. (On p. 182 the electrodjaiamic energy 
is quoted with the wrong sign.) 
