THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
799 
different configuration of an Amj^erean magnetic moleculej the circulation which 
corresponds most closely to the current is more allied to a generalized momentum. 
The energies of magnetic vortex atoms would have to be introduced with changed 
sign into the modified equation of Least Action, and this will involve the presence in 
the modified function of terms containing the electric generalized velocities in the 
first degree. Unless the cross sections of the rings are very small compared with 
their diameters, there will also occur terms involving products of the strengths of 
the vortices and the velocities of the movements of the rings. For two stationary 
thin rigid cores of very narrow section, the mutual forcive due to fluid pressure will 
thus be equal but opposite to the forcive between the corresponding electric currents ; 
the general features of this result are in fact easily verified by consideration of the 
distribution of velocity, and therefore of pressure, in the steady fluid motion of the 
medium. 
107. The serious difficulty pi’esents itself that the mutual attractions of natural 
magnets are actually in the same direction as those of the equivalent electric currents, 
and not, as would appear from this theorem, in the opposite direction. In the first 
place however, the theorem is proved only for rigid cores, held in the circulating- 
fluid medium, and the forcive in question is simply the resultant of fluid pressures 
f)ver the surfaces of the cores. In tlie case of vortex atoms with vacuous cores, such 
a pressure would not exist at all. And when we consider individual molecules, the 
question is also mixed up with the unsolved problem of tlie nature of the inertia of a 
vortex molecule. 
It may be of use to examine separately the distribution of kinetic energy whicli 
the presence of two vortex aggregates implies in the medium surrounding them and 
between them, as distinguished from the kinetic energy inside them which is in 
direct relation wnth intermolecular forces. Let us take Lord Kelvin’s illustration, 
a set of open rigid tubes in a frictionless fluid, through each of which there is circu¬ 
latory motion. “When any change is allowed in the relative positions of two tubes 
by whicii work is done, a diminution of kinetic energy of the fluid is produced within 
the tubes, and at the same time an augmentation of its kinetic energy in the external 
space. The former is equal to double the work done ; the latter is equal to the wmrk 
done; and so the loss of kinetic energy from the whole hcjuid is equal to the work 
done.”'" The distribution of energy in the medium, outside two vortex aggregates, 
thus varies in the same way and with the same sign as the energy of the field of the 
corresponding magnets, as of course it ought to do. And the question is suggested, 
are we allowed to turn the difficulty as to the nature of the inertia of the vortex 
atoms by considering the magnetic forcive between two permanent aggregates as 
derived from the transformation of the kinetic energy in the medium between them ? 
The motion of the medium between them may be set up by the proper impulsive 
pressures over the surfaces of the aggregates, just as the magnetic field is determined 
* Lord Kelvin, “ Electro.=itatics and Magnetism,” 1872, § 737. 
