Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/297

 to them in the circumference of the adjacent vortex; and it seems, therefore, as if the motion would be discontinuous. Maxwell escaped from this difficulty by imitating a well-known mechanical arrangement. When it is desired that two wheels should revolve in the same sense, an "idle" wheel is inserted between them so as to be in gear with both. The model of the electromagnetic field to which Maxwell arrived by the introduction of this device greatly resembles that proposed by Bernoulli in 1736. He supposed a layer of particles, acting as idle wheels, to be interposed between each vortex and the next, and to roll without sliding on the vortices; so that each vortex tends to make the neighbouring vortices revolve in the same direction as itself. The particles were supposed to be not otherwise constrained, so that the velocity of the centre of any particle would be the mean of the circumferential velocities of the vortices between which it is placed. This condition yields (in suitable units) the analytical equation

where the vector l denotes the flux of the particles, so that its x-component ix, denotes the quantity of particles transferred in unit time across unit area perpendicular to the x-direction. On comparing this equation with that which represents Oersted's discovery, it is seen that the flux l of the movable particles interposed between neighbouring vortices is the analogue of the electric current.

It will be noticed that in Maxwell's model the relation between electric current and magnetic force is secured by a connexion which is not of a dynamical, but of a purely kinematical character. The above equation simply expresses the existence of certain non-holonomic constraints within the system.

If from any cause the rotatory velocity of some of the cellular vortices is altered, the disturbance will be propagated from that part of the model to all other parts, by the mutual