APPLICATION OF VON HELMHOLTZ' THEORY. 345

T

reflection from silver in two distinct ways. In the first place we may suppose, that the period of the free vibrations is such, that throughout the luminous portion of the spectrum, and some distance beyond it and on either side, 7 lies between 7, and T2; or in the second place we may suppose, that throughout this range TT3. Now metals reflect rays of dark heat1 in much the same way as they reflect light; accordingly if we adopted the first hypothesis, it would be necessary to suppose, that the free period of the matter vibrations, lies below the infra-red portion of the spectrum; if on the other hand, we adopted the second hypothesis, it would be necessary to suppose, that corresponds to a point in or above the ultra-violet portion of the spectrum. To explain reflection from steel, we must suppose that x is such, that throughout the luminous portion of the spectrum and some distance beyond, 7 is less than T1, or lies between T2 and T3. To explain reflection from copper, we must suppose that either 1 or 7 corresponds to a point of the spectrum intermediate between the red and yellow, since in going up the spectrum, the real part of μ passes through zero, from a negative to a positive value. But in the case of zinc, the real part of μ2 begins by being positive, and then passes through zero to a negative value at a point between the blue and violet. The theory in its present form is therefore not applicable to zinc. It is however necessary to point out, that the theory which has been developed, only applies to a medium having a single absorption band; whereas there is no a priori reason why metals should not possess several. A theory such as von Helmholtz' could be extended, so as to apply to a medium having a number of absorption bands; and there can be little doubt, that the real part of μ would be given by an expression of much the same form, as that furnished by Lord Kelvin's theory.

388. The investigations of the last two Chapters, will give the reader some idea of the various theories relating to the mutual reaction between ether and matter, which have been proposed to explain dispersion and metallic reflection. Further information upon this subject, will be found in Glazebrook's Report on Optical Theories, where a variety of theories due to Lommel, Voigt, Ketteler and others are considered. It must however be con

1 Magnus, Pogg. Ann. Vol. cxxxix.

2 Brit. Assoc. Rep. 1886.

fessed, that most of these theories are of a somewhat tentative and unsatisfactory character; and depend to a great extent upon unproved hypotheses and assumptions made during the progress of the work, for the purpose of obtaining certain analytical results. The fundamental hypothesis, first suggested by Stokes', and afterwards more fully developed by Sellmeier', that these phenomena are due to the fact, that some of the free periods of the vibrations of the molecules of matter fall within the limits of the periods of the visible spectrum, is deserving of attentive consideration and development. This hypothesis is quite independent of any suppositions, which may be made respecting the physical constitution of the ether; since any medium, which is capable of propagating waves, would produce vibrations of the molecules of the matter embedded in it, of the same kind as those we have been discussing.

389. We shall see in the next Chapter, that the electromagnetic theory of light presupposes the existence of a medium or ether; and that the general equations of the electromagnetic field show, that the motion of this medium is governed by equations, which are nearly identical with those furnished by the elastic solid theory. When electromagnetic waves impinge upon the molecules of a material substance, the latter are thrown into a state of vibration, and by making additional assumptions respecting the mutual reaction of ether and matter, we may translate many of the investigations based upon the elastic solid theory, into the language of the electromagnetic theory. Moreover most transparent bodies are dielectrics, whilst metals are conductors of electricity; and certain metals such as iron, cobalt and nickel are strongly magnetic. We should therefore be led to expect, that there would be a marked difference between the propagation of electromagnetic waves in dielectrics on the one hand, and in metals on the other hand. Unfortunately the electromagnetic theory, in the form in which it has hitherto been developed, does not readily lend itself to an explanation of dispersion and metallic reflection; and it must be admitted these phenomena have not as yet been satisfactorily accounted for.

1 Phil. Mag., March 1860, p. 196.

2 Pogg. Ann. Vols. CXLII. p. 272; CXLV. pp 399, 520; CXLVII. pp. 386, 525.

CHAPTER XIX.

THE ELECTROMAGNETIC THEORY.

390. THE electromagnetic theory of light, which was first proposed by the late Prof. Clerk-Maxwell, supposes that the sensation of light is produced by means of an electromagnetic disturbance, which is propagated in a medium; and we cannot do better than to give the fundamental idea of this theory in Maxwell's own words1:

"To fill all space with a new medium, whenever any new phenomenon is to be explained, is by no means philosophical, but if the study of two different branches of science has independently suggested the idea of a medium, and if the properties which must be attributed to the medium in order to account for electromagnetic phenomena, are of the same kind as those which we attribute to the luminiferous medium in order to account for the phenomena of light, the evidence of the physical existence of the medium will be considerably strengthened.

"But the properties of bodies are capable of quantitative measurement. We therefore obtain the numerical value of some property of the medium, such as the velocity with which a disturbance is propagated through it, which can be calculated from electromagnetic experiments, and observed directly in the case of light. If it should be found that the velocity of propagation of electromagnetic disturbances is the same as the velocity of light, and this not only in air, but in other transparent media, we shall have strong reasons for believing that light is an electromagnetic phenomenon, and that a combination of the

1 Electricity and Magnetism, Vol. 11. p. 383.

optical with the electrical evidence will produce a conviction of the reality of the medium, similar to that which we obtain, in the case of other kinds of matter, from the combined evidence of the senses."

391. We shall now proceed to apply the general equations of the electromagnetic field, to obtain the velocity of propagation of an electromagnetic disturbance.

The equations of electromotive force are1

392. If the medium is magnetically isotropic, the magnetic force and the magnetic induction will be connected together by the equations

α = μα,

where μ is the magnetic permeability of the medium.

1 Electricity and Magnetism, Vol. II. Chapter IX.

(4),

EQUATIONS OF THE ELECTROMAGNETIC FIELD. 349

393. If the medium were electrostatically isotropic, the electromotive force in any direction, would be proportional to the electric displacement in the same direction; but if the medium is æolotropic, the relation between electromotive force and electric displacement will depend upon the peculiar constitution of the medium. We have already pointed out, that all doubly-refracting media possess three rectangular planes of symmetry; and we shall now show, that double refraction can be explained by supposing, that the medium is electrostatically æolotropic.

If the axes of symmetry are the axes of coordinates, the equations connecting the electromotive force and electric displacement may be written

P=4πf|K1, Q=4πg/K2, R= 4πh/K2.........................(5), where K1, K,, K, are the three principal electrostatic capacities.

If the medium were a conductor, the equations between the electromotive force and the conduction current would be

where C1, C2, C, are the three principal conductivities. If we suppose the medium isotropic as regards conduction, the three C's will be equal.

The equations connecting the true current, with the electric displacement and conduction current, are

u=ƒ+p, v=ġ+q, w=h+r...............(7).

Since most transparent media are good insulators, we shall suppose that the conduction current is zero, which requires that C1 = C1 = C1 = 0.

394. We can now obtain the equations of electric displacement.