Clerk Maxwell's electromagnetic theory

by H. A. Lorentz

sin (i - r) / sin (i + r)

and

tg (i - r) / tg (i + r),

if i is the angle of incidence and r the angle of refraction; and it is remarkable that, of the two rival theories, one led to the expression with the sines when the other required that with the tangents, and conversely. In connexion with this Fresnel supposed the vibrations of plane polarized light to be at right angles to the plane of polarization, whereas Neumann wanted them to be parallel to that plane.

Here was a problem that long baffled the efforts of physicists, and many attempts were made to determine experimentally the direction of the vibrations. One cannot say that the result has been very satisfactory and the question remained open until Maxwell's theory settled it once for all.

I have enumerated some only of the difficulties with which we had to struggle. I could have mentioned similar problems that arose in the theory of double refraction and I may add that in some cases longitudinal vibrations intruded themselves and complicated the theory.

Maxwell relieved us of all these doubts and uncertainties. By his bold assumption that in a non-conducting body, in a dielectric as he called it, there can exist what is truly a motion of electricity, and that, if this motion, the dielectric displacement, is taken into account, electricity can always be said to move as an incompressible fluid, the open currents and the longitudinal vibrations that were closely allied to them were made to vanish from the scene. Further, the optical behaviour of non-conducting substances was shown to depend on two properties, each characterized by a physical constant, the dielectric constant, or Faraday's specific inductive capacity, and the magnetic permeability. It is true that the way in which these constants are determined by the constitution of matter, by the structure of molecules and atoms, was not considered and that, so far, they were no less inaccessible than the ethereal density and elasticity of the old theories, but there was this important difference that, whereas these latter constants had no connexion with any other phenomena, the dielectric constant and the magnetic permeability can be measured by means of statical experiments, so that, at least in certain simple cases, we can deduce the optical properties of a substance from wholly different data. It was found that in the new theory the treatment of the reflexion problem was much like that in the old one; one is led to the two formulae which I recalled to you, if one supposes either the dielectric constant or the magnetic permeability to be the same in the two substances. The choice between these alternative suppositions again entailed a decision concerning the direction of the vibrations with respect to the plane of polarization, but the choice was not doubtful now, as it had been ascertained experimentally that the ratios between the magnetic permeabilities of transparent substances are little different from unity, whereas the dielectric constants diverge to a much greater extent. It was therefore at once established that the electric vibrations are normal to the plane of polarization. This implies that the magnetic vibrations are in that plane, so that, in a sense, the contending parties both had their will.

In the case of crystals it became certain that their double refraction is due to an inequality of the dielectric properties in different directions.

So, many difficulties and outstanding problems melted away as snow before the sun. Indeed, a reviewer in Nature actually compared Maxwell's work to the sun, his only criticism being that there are spots on the sun itself, which, however, "are not visible save to those whose eyes can bear the full glare of the glowing orb." My eyes certainly were not as strong as that. I could not see the spots, but what I could see was that the sun was not entirely unclouded; what sun always was? It was not always easy to grasp Maxwell's ideas, and one feels a want of unity in his book, due to the fact that it faithfully reproduces his gradual transition from old to new ideas. When we read what Maxwell says of Ampère and Faraday, of the former having removed all traces of the scaffolding by which he had built up a perfect demonstration of his law, whereas Faraday "shews us his unsuccessful as well as his successful experiments, and his crude ideas as well as his developed ones," we feel that, great though the difference may be between the Experimental Researches and Maxwell's largely mathematical Treatise, yet the two works were written in the same spirit. In fact, Maxwell repeatedly expresses his indebtedness to Faraday, from whom he had borrowed part of his fundamental ideas, so that, when there is question of Maxwell's theory, we must often think of Faraday also.

Maxwell's followers, of whom there were many, in this country and elsewhere, have perfected the theory in its form and extended it by the introduction of new ideas. Think, for instance, of Poynting's beautiful and important theorem on the flow of energy, determined at every point by the electric and the magnetic force existing in the field, a theorem that has produced more clearness perhaps than any other and which is now so essential that we can hardly recall the state in which physics was when we did not know it. Yet, notwithstanding all innovations of this kind, we always speak, and with full justice, of "Maxwell's Theory." We continue to do so now that we have been led to introduce electric charges supposed to exist in the interior of molecules and atoms, by which we have come to the theory of electrons. And when we refer to those wonderfully simple equations in which the fundamental laws of electromagnetism are embodied with a conciseness that could never have been dreamed of before, we call them "Maxwell's Equations." Surely, though Maxwell did not use them in their modern form, no name could be more appropriate, for the general relations which they express are those that were constantly in his mind.