286 Prof. Maxwell on the Theory of Molecular Vortices 
perience resistance, so as to waste electrical energy and generate 
heat. 
Now let us suppose the vortices arranged in a medium in any 
arbitrary manner. The quantities i 4 , &e. will then in 
general have values, so that there will at first be electrical cur- 
rents in the medium. These will be opposed by the electrical 
resistance of the medium ; so that, unless they are kept up by a 
continuous supply of force, they will quickly disappear, and we 
shall then have — = =0, &e.; that is, adx+ Bdy+rydz will 
be a complete differential (see equations (15) and (16)) ; so that 
our hypothesis accounts for the distribution of the lines of force. 
In Plate V. fig. 1, let the vertical circle E E represent an elec- 
tric current flowing from copper C to zinc Z through the con- 
ductor E EH’, as shown by the arrows. 
Let the horizontal circle M M' represent a line of magnetic 
force embracing the electric circuit, the north and south direc- 
tions bemg indicated by the ines 8 N and NS. 
Let the vertical circles V and V’ represent the molecular vor- 
tices of which the lme of magnetic force is the axis. V revolves 
as the hands of a watch, and V’ the opposite way. 
It will appear from this diagram, that if V and V! were conti- 
guous vortices, particles placed between them would move down- 
wards; and that if the particles were forced downwards by any 
cause, they would make the vortices revolve as in the figure. 
We have thus obtained a point of view from which we may regard 
the relation of an electric current to its lines of force as analogous 
to the relation of a toothed wheel or rack to wheels which it 
drives. 
In the first part of the paper we investigated the relations of 
the statical forces of the system. We have now considered the 
connexion of the motions of the parts considered as a system of 
mechanism. It remains that we should investigate the dynamics 
of the system, and determine the forces necessary to produce 
viven changes in the motions of the different parts. 
Prop. V1.—To determine the actual energy of a portion of a 
medium due to the motion of the vortices within it. 
Let «, 8, y be the components of the circumferential velocity, 
as in Prop. II., then the actual energy of the vortices in unit of 
volume will be proportional to the density and to the square of 
the velocity. As we do not know the distribution of density and 
velocity in each vortex, we cannot determine the numerical value 
of the energy directly; but since y also bears a constant though 
unknown ratio to the mean density, let us assume that the energy 
