James Clerk Maxwell and Modern Physics

by Richard Glazebrook

The cells A and B may be compared to two cog-wheels placed close together, which we wish to turn in the same direction. If the cogs can interlock, as in [Fig. 2], this is impossible: consecutive wheels in the train must move in opposite directions.

Fig. 3.

But in many machines the desired end is attained by inserting between the two wheels A and B a third idle wheel C, as shewn in [Fig. 3]. This may be very small, its only function is to transmit the motion of A to B in such a way that A and B may both turn in the same direction. It is not necessary that there should be cogs on the wheels; if the surfaces be perfectly rough, so that no slipping can take place, the same result follows without the cogs.

Guided by this analogy Maxwell extended his model by supposing each cell coated with a number of small particles which roll on its surface. These particles play the part of the idle wheels in the machine, and by their rolling merely enable the adjacent parts of two cells to move in opposite directions.

Consider now a number of such cells and their idle wheels lying in a plane, that of the paper, and suppose each cell is rotating with the same uniform angular velocity about an axis at right angles to that plane, each idle wheel will be acted on by two equal and opposite forces at the ends of the diameter in which it is touched by the adjacent cells; it will therefore be set in rotation, but there will be no force tending to drive it onwards; it does not matter whether the axis on which it rotates is free to move or fixed, in either case the idle wheel simply rotates. But suppose now the adjacent cells are not rotating at the same rate. In addition to its rotation the idle wheel will be urged onward with a velocity which depends on the difference between the rotations, and, if it can move freely, it will move on from between the two cells. Imagine now that the interstices between the cells are fitted with a string of idle wheels. So long as the adjacent cells move with different velocity there will be a continual stream of rolling particles or idle wheels between them. Maxwell in the paper considered these rolling particles to be particles of electricity. Their motion constitutes an electric current. In a uniform magnetic field there is no electric current; if the strength of the field varies, the idle wheels are set in motion and there may be a current.

These particles are very small compared with the magnetic vortices. The mass of all the particles is inappreciable compared with the mass of the vortices, and a great many vortices with their surrounding particles are contained in a molecule of the medium; the particles roll on the vortices without touching each other, so that so long as they remain within the same molecule there is no loss of energy by resistance. When, however, there is a current or general transference of particles in one direction they must pass from one molecule to another, and in doing so may experience resistance and generate heat.

Maxwell states that the conception of a particle, having its motion connected with that of a vortex by perfect rolling contact, may appear somewhat awkward. “I do not bring it forward,” he writes, “as a mode of connection existing in Nature, or even as that which I would willingly assent to as an electrical hypothesis. It is, however, a mode of connection which is mechanically conceivable and easily investigated, and it serves to bring out the actual mechanical connections between the known electro-magnetic phenomena, so that I venture to say that anyone who understands the provisional and temporary character of this hypothesis will find himself rather helped than hindered by it in his search after the true interpretation of the phenomena.”

The first part of the paper deals with the theory of magnetism; in the second part the hypothesis is applied to the phenomena of electric currents, and it is shown how the known laws of steady currents and of electro-magnetic induction can be deduced from it. In Part III., published January and February, 1862, the theory of molecular vortices is applied to statical electricity.

The distinction between a conductor and an insulator or dielectric is supposed to be that in the former the particles of electricity can pass with more or less freedom from molecule to molecule. In the latter such transference is impossible, the particles can only be displaced within the molecule with which they are connected; the cells or vortices of the medium are supposed to be elastic, and to resist by their elasticity the displacement of the particles within them. When electrical force acts on the medium this displacement of the particles within each molecule takes place until the stresses due to the elastic reaction of the vortices balance the electrical force; the medium behaves like an elastic body yielding to pressure until the pressure is balanced by the elastic stress. When the electric force is removed the cells or vortices recover their form, the electricity returns to its former position.