converse is the case. The theory is also incapable of accounting for the polarization of light, and is now universally condemned as untenable.

The undulatory theory was first proposed by Huygens in 1678, and in the hands of Young, Fresnel and others, has been found capable of furnishing so satisfactory an explanation of experimental results, that it is now universally accepted as the true theory of light. The undulatory theory assumes, that all space is filled with a medium called the luminiferous ether, which is capable of being thrown into a state of vibration or wave motion, and of transmitting such vibrations with a definite velocity. Whenever any substance, which is capable of exciting periodic motion in the ether, exists in any portion of space, it is supposed that waves consisting of periodic vibrations are continually propagated in all directions. When the waves reach the retina of the eye, the ether in contact with it is set in motion, and a certain. effect is produced upon the retina, which is transmitted to the brain by means of the optic nerve, and gives rise to the sensation of light.

3. It must not however be supposed, that all vibrations which the ether is capable of executing, necessarily affect the eye. In the Theory of Sound, which presents many points of analogy with the Theory of Light, it is well known that it is extremely easy to produce a disturbance in the air, which possesses all the physical properties of a wave of sound, but which nevertheless is incapable of producing any impression upon the ear. In fact the ear is only capable of taking cognizance of waves of sound, whose periods lie within certain definite limits. Similarly the eye is only capable of being affected by ethereal waves, whose periods lie between certain limits, which are far narrower than the corresponding limits in the case of Sound, and which in acoustical language may be described as lying within an octave. At the same time it is certain that ethereal waves exist, whose periods lie outside the limits of the extreme red and violet rays of the spectrum, which possess all the physical properties of waves of light, but whose existence can only be discovered by the thermal or chemical effects which they produce.

The luminiferous ether is supposed to exist not only in air, liquids, and ultraterrestrial space, but also in solid bodies. Molecular theories furnish strong grounds for the conclusion, that the

THE LUMINIFEROUS ETHER.

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molecules of even the densest and hardest bodies do not form an absolutely compact mass, but that interstices exist between them, which are filled with ether; and it is owing to this cause, that hard transparent substances like glass and diamond are capable of transmitting light. If therefore we assume that a hard and dense substance, such as glass, contains interstices which are filled with ether, it would be somewhat inconsistent to suppose, that the opacity of a soft substance, like tallow, is due to the fact, that it does not contain ether. We must therefore look for an explanation. of the opacity of tallow or wax, as being due to some peculiar action of the molecular structure of such materials, which prevents the ether contained in them from transmitting vibrations.

If we were fully acquainted with the physical properties of the ether and its relation to ponderable matter, the explanation of optical phenomena would become a mere question of mathematical analysis. We should simply have to translate the physical properties of the ether into mathematical language, and should thereby obtain the equations of motion and the boundary conditions; and the solution of these equations would furnish a complete theoretical explanation of every experimental result. But although there are abundant grounds for justifying our belief in the existence of the ether, we are almost completely in the dark respecting its properties. Accordingly, the only means at our disposal for obtaining any information upon this question, is to adopt the inductive method of making some hypothesis which is dynamically sound and physically possible, and which is capable of being expressed in a mathematical form, and then to compare the results to which theory leads us with known experimental facts. If the results of our theory are wholly inconsistent with experiment, the theory must be abandoned; but if our theoretical results are wholly or partially in accordance with experiment, we shall be justified in concluding that our theory, if not absolutely true, may at any rate contain a germ of truth.

4. The first rigorous dynamical theory of light was proposed by Green in 1837. He supposed that the ether is a medium which is capable of resisting compression and distortion; and he showed that when the medium is isotropic, the equations of motion are the same as those of an isotropic elastic solid, and contain two independent constants, one of which measures the resistance to compression, and the other the resistance to distortion. Green

was also led to assume from physical considerations, that the first constant is very large in comparison with the second. This has sometimes been interpreted to mean that the ether is almost incompressible, but an assumption of this kind is not an essential part of Green's theory. The theory would be satisfied, if the ether were more compressible than the most highly compressible gas; all that is necessary is, that the ratio of the resistance to compression to the resistance to distortion should be very large. Green's theory explains fairly well the propagation of light in isotropic media, but it fails to furnish a satisfactory theory of double refraction, and takes no account of rotatory polarization and dispersion.

5. The second class of theories, are theories based upon the mutual reaction of ether and matter. When a wave of light impinges upon a transparent or opaque substance, it is supposed that the vibrations of the ether set the molecules of the matter composing the substance into a state of vibration, and that these vibrations modify the motion of the ether. If the ether be regarded as a substance possessing a density, which is finite though excessively small compared with the densities of substances ordinarily met with, the action of the matter will produce certain forces which affect the ether. It has been proved experimentally, that if the light which is emitted from certain substances when incandescent (such as burning sodium), be transmitted through the vapour of those substances, light will be absorbed. The explanation of this phenomenon, which was first suggested by Stokes', depends upon a theorem due to Sir J. Herschel, that when a dynamical system is acted upon by a periodic force, whose period is equal, or nearly so, to one of the periods of the free vibrations of the system, the corresponding forced vibration will be large. Now sodium vapour when incandescent, emits light of a certain definite period, which is consequently one of the free periods of the vibrations of sodium vapour. Accordingly, when light from a sodium flame passes through sodium vapour, the molecules of the vapour are thrown into a violent state of vibration; and as the energy required for the maintenance of these vibrations must be supplied by the waves of light, it follows that a comparatively small portion of the energy which enters the vapour emerges from it, and therefore light is absorbed. The

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

DIFFERENT THEORIES OF LIGHT.

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foregoing illustration will give some idea of the way in which the vibrations of ether are affected by the presence of matter.

6. The third theory, is the electromagnetic theory due to the late Professor J. Clerk-Maxwell, which supposes that light is the effect of an electromagnetic disturbance. This theory not only explains the propagation of light in isotropic media, but furnishes the most satisfactory theory of double refraction which has yet been proposed.

The early death of Maxwell at the age of forty-nine prevented him from elaborating and completing this theory, which as it left his hands, took no account of dispersion, nor of rotatory polarization produced by quartz or turpentine; but several important additions to the theory have been made during recent years, which will be considered in the concluding chapters of this work.

7. To commence this treatise with a discussion of the various theories of light, which have been briefly touched upon in the foregoing paragraphs, would throw a considerable strain upon the mathematical resources of the reader; but inasmuch as there are a variety of optical phenomena, which are capable of being explained upon the hypothesis of a medium which is capable of propagating waves, without entering into any speculations concerning the physical properties of the medium, I think that the best course to adopt will be to dispense as far as possible with dynamical theories for the present, and to endeavour to explain the phenomena which present themselves by means of the geometrical properties of wave motion. We shall thus be able to explain Interference, Colours of Thick and Thin Plates, Diffraction, and Polarization. Double Refraction cannot be satisfactorily discussed without a theory of some kind; but having given an account of Fresnel's theory, which although dynamically unsound, is of great historical interest, we shall be able to investigate the geometrical properties of Fresnel's wave surface, and the production of coloured rings by thin crystalline plates; and we shall then be in a better position to understand the more theoretical portions of the subject.

8. When a source of light exists in an isotropic medium, spherical waves concentric with the source are propagated throughout the medium; and if the effect, which these waves produce at some portion of space, whose greatest linear dimension is small in

comparison with its distance from the source, be observed, the waves may be regarded as approximately plane. We are thus led in the first instance to study plane waves.

Let us therefore suppose, that a train of plane waves is propagated in some given direction, which we shall choose as the axis of a; then if v be the displacement of the medium, we may write

A discussion of the kinematical properties of wave motion is given in my Elementary Treatise on Hydrodynamics and Sound, § 76, to which the reader is referred. It will be observed, that the right-hand side of (1) contains four constants A, V, X, e; we may also if we please introduce the period in the place of V or λ, because VTλ; accordingly (1) may be written in the forms

9. We must now enquire, how these four constants are related to the physical properties of a wave.

The quantity e is called the phase of the wave, and fixes its position with respect to the point assumed as the origin. This constant is therefore a purely geometrical one.

The quantity V is called the velocity of propagation of the wave, and measures the velocity with which light is travelling in the medium. In isotropic media, V is independent of the direction of the wave, but in æolotropic media, V is a function of the direction.

That light travels with a finite velocity, was first established in 1676 by the Danish astronomer Olaus Römer, who observed that when the planet Jupiter was nearest to the Earth, the eclipses of Jupiter's moons happened earlier than they ought to have done according to the astronomical tables; whilst when Jupiter was farthest from the Earth, they happened later. He therefore concluded that the difference between the observed and calculated times was due to the fact, that light occupies a finite time in travelling from one point to another, and he calculated that the velocity of light in vacuo was 3023 × 105 metres per second.