W. Thomson

Thomson had compared electric force to the displacement in an elastic solid.

Faraday had likened the particles of a ponderable dielectric to small conductors embedded in an insulating medium[21].

He had supposed that when the dielectric is subjected to an electrostatic field, there is a displacement of electric charge on each of the small conductors.

The motion of these charges, when the field is varied, is equivalent to an electric current. From this, Maxwell derived the principle, which became of cardinal importance in his theory, that variations of displacement are to be counted as currents.

But in adopting the idea, he altogether transformed it; for Faraday’s conception of displacement was applicable only to ponderable dielectrics, and was in fact introduced solely in order to explain why the specific inductive capacity of such dielectrics is different from that of free aether; whereas according to Maxwell there is displacement wherever there is electric force, whether material bodies are present or not.

The difference between the conceptions of Faraday and Maxwell in this respect may be illustrated by an analogy drawn from the theory of magnetism. When a piece of iron is placed in a magnetic field, there is induced in it a magnetic distribution, say of intensity I.

This induced magnetization exists only within the iron, being zero in the free aether outside.

The vector I may be compared to the polarization or displacement, which according to Faraday is induced in dielectrics by an electric field; and the electric current constituted by the variation of this polarization is then analogous to ∂I/∂t. But the entity which was called by Maxwell the electric displacement in the dielectric is analogous not to I, but to the magnetic induction B: the Maxwellian displacement-current corresponds to ∂B/∂t, and may therefore have a value different from zero even in free aether.

The term ‘displacement’ was thus introduced. But that word was not well-chosen.

In the early models of the aether, it represented an actual displacement. But in later investigations, it showed a change of structure rather than of position in the elements of the aether.

Maxwell supposed the electromotive force acting on the electric particles to be connected with the displacement D which accompanies it, by an equation of the form

where c1 denotes a constant which depends on the elastic properties of the cells.

The displacement-current Ḋ must now be inserted in the relation which connects the current with the magnetic force; and thus we obtain the equation

where the vector S, which is called the total current, is the sum of the convection-current i and the displacement-current Ḋ.

By performing the operation div on both sides of this equation, it is seen that the total current is a circuital vector, In the model, the total current is represented by the total motion of the rolling particles; and this is conditioned by the rotations of the vortices in such a way as to impose the kinematic relation

Having obtained the equations of motion of his system of vortices and particles, Maxwell proceeded to determine the rate of propagation of disturbances through it. He considered in particular the case in which the substance represented is a dielectric, so that the conduction-current is zero. If, moreover, the constant μ be supposed to have the value unity, the equations may be written

Eliminating E, we see[22] that H satisfies the equations

But these are precisely the equations which the light-vector satisfies in a medium in which the velocity of propagation is c1: it follows that disturbances are propagated through the model by waves which are similar to waves of light, the magnetic (and similarly the electric) vector being in the wave-front. For a plane-polarized wave propagated parallel to the axis of z, the equations reduce to

whence we have

these equations show that the electric and magnetic vectors are at right angles to each other.

The question now arises as to the magnitude of the constant c1.[23] This may be determined by comparing different expressions for the energy of an electrostatic field. The work done by an electromotive force E in producing a displacement D is

per unit volume, since E is proportional to D. But if it be assumed that the energy of an electrostatic field is resident in the dielectric, the amount of energy per unit volume may be calculated by considering the mechanical force required in order to increase the distance between the plates of a condenser, so as to enlarge the field comprised between them.

The result is that tho energy per unit volume of the dielectric is εE′2/8π, where ε denotes the specific inductive capacity of the dielectric and E′ denotes the electric force, measured in terms of the electrostatic unit: if E denotes the electric force expressed in terms of the electrodynamic units used in the present investigation, we have E = cE′, where e denotes the constant which[24] occurs in transformations of this kind. The energy is therefore εE2/8πc2 per unit volume. Comparing this with the expression for the energy in terms of E and D, we have

Therefore the constant c1 has the value cε-

. Thus the result is obtained that the velocity of propagation of disturbances in Maxwell’s medium is cε-

, where ε denotes the specific inductive capacity and c denotes the velocity for which Kohlrausch and Weber had found[25] the value 3·1 x 1010 cm./sec.

Now by this time the velocity of light was known, not only from the astronomical observations of aberration and of Jupiter’s satellites, but also by direct terrestrial experiments.

In 1849 Hippolyte Louis Fizeau[26] had determined it by rotating a toothed wheel so rapidly that a beam of light transmitted through the gap between two teeth and reflected back from a mirror was eclipsed by one of the teeth on its return journey. Tho velocity of light was calculated from the dimensions and angular velocity of the wheel and the distance of the mirror; the result being 3·15 1010 cm./sec.[27]

Maxwell was impressed, as Kirchhoff had been before him, by the close agreement between the electric ratio c and the speed of light[28].

He demonstrated that the propagation of electric disturbance resembles that of light. He thus asserted the identity of the two phenomena.

“Light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”

Thus he answered Priestley’s question:[29] “Is there any electric fluid sui generis at all, distinct from the aether?”

The presence of the dielectric constant ε in the expression cε-

This Maxwell had obtained for the velocity of propagation of electromagnetic disturbances, suggested a further test of the identity of these disturbances with light: for the velocity of light in a medium is known to be inversely proportional to the refractive index of the medium, and therefore the refractive index should be, according to the theory, proportional to the square root of the specific inductive capacity. At the time, however, Maxwell did not examine whether this relation was confirmed by experiment.

In what has preceded, the magnetic permeability μ has been supposed to have the value unity. If this is not the case, the velocity of propagation of disturbance may be shown, by the same analysis, to be cε-

; so that it is diminished when μ is greater than unity, i.e., in paramagnetic bodies. This inference had been anticipated by Faraday: “Nor is it likely,” he wrote,[30] “that the paramagnetic body oxygen can exist in the air and not retard the transmission of the magnetism.”