HAVING been invited by President Gilman to deliver a course of lectures in the Johns Hopkins University after the meeting of the British Association in Montreal in 1884, on a subject in Physical Science to be chosen by myself, I gladly accepted the invitation. I chose as subject the Wave Theory of Light with the intention of accentuating its failures; rather than of setting forth to junior students the admirable success with which this beautiful theory had explained all that was known of light before the time of Fresnel and Thomas Young, and had produced floods of new knowledge splendidly enriching the whole domain of physical science. My audience was to consist of Professorial fellow-students in physical science; and from the beginning I felt that our meetings were to be conferences of coefficients, in endeavours to advance science, rather than teachings of my comrades by myself. I spoke with absolute freedom, and had never the slightest fear of undermining their perfect faith in ether and its light-giving waves: by anything I could tell them of the imperfection of our mathematics; of the insufficiency or faultiness of our views regarding the dynamical qualities of ether; and of the overwhelmingly great difficulty of finding a field of action for ether among the atoms of ponderable matter. We all felt that difficulties were to be faced and not to be evaded; were to be taken to heart with the hope of solving them if possible; but at all events with the certain assurance that there is an explanation of every difficulty though we may never succeed in finding it.

The most important branch of physics which at present makes demands upon molecular dynamics seems to me to be the wave theory of light. When I say this, I do not forget the one great branch of physics which at present is reduced to molecular dynamics, the kinetic theory of gases. In saying that the wave theory of light seems to be that branch of physics which is most in want, which most imperatively demands, applications, of molecular dynamics just now, I mean that, while the kinetic theory of gases is a part of molecular dynamics, is founded upon molecular dynamics, works wholly within molecular dynamics, to it molecular dynamics is everything, and it can be advanced solely by molecular dynamics; the wave theory of light is only beginning to demand imperatively applications of that kind of dynamical science.

The dynamics of the wave theory of light began very molecularly in the hands of Fresnel, was continued so by Cauchy, and to some degree, though much less so, in the hands of Green. It was wholly molecular dynamics, but of an imperfect kind in the hands of Fresnel. Cauchy attempted to found his mathematical investigations on a rigorous molecular treatment of the subject. Green almost wholly shook off the molecular treatment, and worked out all that was to be worked out for the wave theory of light, by the dynamics of continuous matter.

DYNAMICAL ILLUSTRATIONS OF THE MAGNETIC AND THE HELIÇOIDAL ROTATORY EFFECTS OF TRANSPARENT BODIES ON POLARIZED LIGHT

The elastic reaction of a homogeneously strained solid has a character essentially devoid of all heliçidal and of all dipolar asymmetry. Hence the rotation of the plane of polarization of light passing through bodies which either intrinsically possess the heliçidal property (syrup, oil of turpentine, quartz crystals, &c), or have the magnetic property induced in them, must be due to elastic reactions dependent on the heterogeneousness of the strain through the space of a wave, or to some heterogeneousness of the luminous motions dependent on a heterogeneousness of parts of the matter of lineal dimensions not infinitely small in comparison with the wave length. An infinitely homogeneous solid could not possess either of those properties if the stress at any point of it was influenced only by parts of the body touching it; but if the stress at one point is directly influenced by the strain in parts at distances from it finite in comparison with the wave length, the heliçoidal property might exist, and the rotation of the plane of polarization, such as is observed in many liquids and in quartz crystals, could be explained as a direct dynamical consequence of the statical elastic reaction called into play by such a strain as exists in a wave of polarized light.

[This was a double lecture; but as the substance of the first part, with amplification partly founded on experimental discoveries by many workers since it was delivered, has been already reproduced in dated additions on pp. 148—157 and 176—184 above, only the second part is here given.]

I want now to go somewhat into detail as to absolute magnitudes of masses and energies, in order that there may be nothing indefinite in our ideas upon this part of our subject; and I commence by reading and commenting on an old article of mine relating to the energy of sunlight and the density of ether.

[Nov. 20, 1899…March 28, 1901. From now, henceforth till the end of the Lectures, sections will be numbered continuously.]

NOTE ON THE POSSIBLE DENSITY OF THE LUMINIFEROUS MEDIUM AND ON THE MECHANICAL VALUE OF A CUBIC MILE OF SUNLIGHT

[From Edin. Royal Soc. Trans., Vol. xxi. Part I. May, 1854; Phil. Mag. ix. 1854; Comptes Rendus, xxxix. Sept. 1854; Art. LXVII. of Math. and Phys. Papers.]

Molar

§ 1. That there must be a medium forming a continuous material communication throughout space to the remotest visible body is a fundamental assumption in the undulatory Theory of Light. Whether or not this medium is (as appears to me most probable) a continuation of our own atmosphere, its existence is a fact that cannot be questioned, when the overwhelming evidence in favour of the undulatory theory is considered; and the investigation of its properties in every possible way becomes an object of the greatest interest.

Part I. In the first place, I will take up the equations of motion of an elastic solid. I assume that the fundamental principles are familiar to you. At the same time, I should be very glad if any person present would, without the slightest hesitation, ask for explanations if anything is not understood. I want to be on a conferent footing with you, so that the work shall be rather something between you and me, than something in which I shall be making a performance before you in a matter in which many of you may be quite as competent as I am, if not more so.

I want, if we can get something done in half an hour, on these problems of molar dynamics as we may call it, to distinguish from Molecular dynamics, to come among you, and talk with you for a few moments, and take a little rest; and then go on to a problem of molecular dynamics to prepare the way for motions depending on mutual interference among particles under varying circumstances that may perhaps have applications in physical science and particularly to the theory of light.

Molar

The fundamental equations of equilibrium of elastic solids are, of course, included in D'Alembert's form of the equations of motion. I shall keep to the notation that is employed in Thomson and Tait's Natural Philosophy, which is substantially the same notation as is employed by other writers.

Molecular

Returning to our model, we shall have in a short time a state of things not very different from simple harmonic motion, if we get up the motion very gradually. We have now an exciting vibration of shorter period than the shortest of the natural periods. We must keep the vibrator going through a uniform range. We are not to augment it, and it will be a good thing to place something here to mark its range. [This done.] Keep it going long enough and we shall see a state of vibration in which each bar will be going in the opposite direction to its neighbour. If we keep it going long enough we certainly will have the simple harmonic motion; and if this period is smaller than the smallest of the three natural periods, we shall, as we know, have the alternate bars going in opposite directions. Now you see a longer-period vibration of the largest mass superimposed on the simple harmonic motion we are waiting for. I will try to help towards that condition of affairs by resisting the vibration of the top particle. In fact, that particle will have exceedingly little motion in the proper state of things (that is to say, when the motion is simple harmonic throughout), and it will be moving, so far as it has motion at all, in an opposite direction to the particle immediately below it.

Molecular

§ 200. Considering how well Rankine's old idea of æolotropic inertia has served us for the theory of double refraction, it naturally occurs to try if we can found on it also a thorough dynamical explanation of the rotation of the plane of polarization of light in a transparent liquid, or crystal, possessing the chiral property. I prepared the way for working out this idea in a short paper communicated to the Royal Society of Edinburgh in Session 1870—71 under the title “On the Motion of Free Solids through a Liquid” which was re-published in the Philosophical Magazine for November 1871 as part of an article entitled “Hydrokinetic Solutions and Observations,” and which constitutes the greater part of Appendix G of the present volume. The extreme difficulty of seeing how atoms or molecules embedded in (ether), an elastic solid could experience resistance to change of motion practically analogous to the quasi-inertia conferred on a solid moving through an incompressible liquid has, until a few weeks ago, prevented me from attempting to explain chiral polarization of light by æolotropic inertia. Now, the explanation is rendered easy and natural by the hypothesis explained in §§ 162—164 above and in §§ 204, 205 below and in Appendix A.

Gravitational matter, according to our ideas of universal gravitation, would be all matter. Now is there any matter which is not subject to the law of gravitation? I think I may say with absolute decision that there is. We are all convinced, with our President, that ether is matter, but we are forced to say that we must not expect to find in ether the ordinary properties of molar matter which are generally known to us by action resulting from force between atoms and matter, ether and ether, and atoms of matter and ether. Here I am illogical when I say between matter and ether, as if ether were not matter. It is to avoid an illogical phraseology that I use the title “gravitational matter.” Many years ago I gave strong reason to feel certain that ether was outside the law of gravitation. We need not absolutely exclude, as an idea, the possibility of there being a portion of space occupied by ether beyond which there is absolute vacuum—no ether and no matter. We admit that that is something that one could think of; but I do not believe any living scientific man considers it in the slightest degree probable that there is a boundary around our universe beyond which there is no ether and no matter. Well, if ether extends through all space, then it is certain that ether cannot be subject to the law of mutual gravitation between its parts, because if it were subject to mutual attraction between its parts its equilibrium would be unstable, unless it were infinitely incompressible.

§ 1. To simplify our problem, by avoiding the interesting subject of alternating electric currents of electricity in a solid conductor dealt with in §§ 9, 19, 29—35 of Art. cii. of my Mathematical and Physical Papers, Vol. III., I suppose for the present the central conductor and the surrounding sheath to be exceedingly thin copper tubes; so thin that the electric current carried by each is uniformly distributed through its substance, with the highest frequency of alternation which we shall have to consider. To simplify farther, by avoiding the exceedingly complex question of electric currents in the water above the cable and wet ground below it, I for the present suppose the outer sheath to be perfectly insulated. This supposition will make exceedingly little difference in respect to the solution of our problem for such frequencies of alternation as are used in submarine signalling; but it makes a vast difference and simplification for the very high frequencies, up to those of the vibrations constituting light, which must be considered. For brevity I shall call the system of two conductors, with air or gutta-percha or other insulating material between them, the cable. For simplicity we shall suppose the cable to be laid straight; and shall specify any place in the cable by x, its distance from any chosen point of reference O in the axis of the inner conductor.

Molar

§ 82. The subject of this Lecture when originally given was “Reflection and Refraction of Light.” I have recently found it convenient to omit “Refraction” from the title because (§ 130 below), if the reflecting substance is transparent, and if we know the laws of propagation of ethereal waves through it, we can calculate the amount and quality of the refracted light for every quality of incident light, and every angle of incidence, when we know the amount and quality of the reflected light. When the reflecting substance is opaque there is no “refracted” light; but, co-periodic with the motion which constitutes the incident light, there is a vibratory motion in the ether among the matter of the reflecting body, diminishing in amplitude according to the exponential law, ∊−mD, with increasing distance D from the interface. When m−1 is equal to 10,000 wave-lengths, say half-a-centimetre, the amplitude of the disturbance at onehalf centimetre inwards from the interface would be ∊−1 of the amplitude of the entering light, and the intensity would be ∊−2, or 1/7·39, of the intensity of the entering light. The substance might or might not, as we please, be called opaque; but it would be so far from being perfectly opaque that both theoretically and experimentally we might conveniently deal with the case according to the ordinary doctrine of “reflected” and “refracted” light.

§ 1. A screen of imperfectly conducting material is as thorough in its action, when time enough is allowed it, as is a similar screen of metal. But if it be tried against rapidly varying electrostatic force, its action lags. On account of this lagging, it is easily seen that the screening effect against periodic variations of electrostatic force will be less and less, the greater the frequency of the variation. This is readily illustrated by means of various forms of idiostatic electrometers. Thus, for example, a piece of paper supported on metal in metallic communication with the movable disc of an attracted disc electrometer annuls the attraction (or renders it quite insensible) a few seconds of time after a difference of potential is established and kept constant between the attracted disc and the opposed metal plate, if the paper and the air surrounding it are in the ordinary hygrometric condition of our climates. But if the instrument is applied to measure a rapidly alternating difference of potential, with equal differences on the two sides of zero, it gives very little less than the same average force as that found when the paper is removed and all other circumstances kept the same. Probably, with ordinary clean white paper in ordinary hygrometric conditions, a frequency of alternation of from 50 to 100 per second will more than suffice to render the screening influence of the paper insensible.