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.

§ 1. According to the well-known doctrine of Aepinus, commonly referred to as the one-fluid theory of electricity, positive and negative electrifications consist in excess above, and deficiency below, a natural quantum of a fluid, called the electric fluid, permeating among the atoms of ponderable matter. Portions of matter void of the electric fluid repel one another; portions of the electric fluid repel one another; portions of the electric fluid and of void matter attract one another.

§ 2. My suggestion is that the Aepinus' fluid consists of exceedingly minute equal and similar atoms, which I call electrions, much smaller than the atoms of ponderable matter; and that they permeate freely through the spaces occupied by these greater atoms and also freely through space not occupied by them. As in Aepinus' theory we must have repulsions between the electrions; and repulsions between the atoms independently of the electrions; and attractions between electrions and atoms without electrions. For brevity, in future by atom I shall mean an atom of ponderable matter, whether it has any electrions within it or not.

§ 3. In virtue of the discovery and experimental proof by Cavendish and Coulomb of the law of inverse square of distance for both electric attractions and repulsions, we may now suppose that the atoms, which I assume to be all of them spherical, repel other atoms outside them with forces inversely as the squares of distances between centres; and that the same is true of electrions, which no doubt occupy finite spaces, although at present we are dealing with them as if they were mere mathematical points, endowed with the property of electric attraction and repulsion.

Molecular

§ 23. Hitherto in all our views we have seen nothing of absolute dimensions in molecular structure, and have been satisfied to consider the distance between neighbouring molecules in gases, or liquids, or crystals, or non-crystalline solids to be very small in comparison with the shortest wave-length of light with which we have been concerned. Even in respect to dispersion, that is to say, difference of propagational velocity for different wave-lengths, it has not been necessary for us to accept Cauchy's doctrine that the spheres of molecular action are comparable with the wavelength. We have seen that dispersion can be, and probably in fact is, truly explained by the periods of our waves of light being not infinitely great in comparison with some of the periods of molecular vibration; and, with this view, the dimensions of molecular structure might, so far as dispersion is concerned, be as small as we please to imagine them, in comparison with wavelengths of light. Nevertheless it is exceedingly interesting and important for intelligent study of molecular structures and the dynamics of light, to have some well-founded understanding in respect to probable distances between centres of neighbouring molecules in all kinds of ponderable matter, while for the present at all events we regard ether as utterly continuous and structureless. It may be found in some future time that ether too has a molecular structure, perhaps much finer than any structure of ponderable matter; but at present we neither see nor imagine any reason for believing ether to be other than continuous and homogeneous through infinitely small contiguous portions of space void of other matter than ether.

Molecular

Prof. Morley has already partially solved the definite dynamical problem that I proposed to you last Wednesday (p. 103 above) so far as determining four of the fundamental periods; and you may be interested in knowing the result. He finds roots, κ−2, κ−2, &c, = 3·46, 1·005, ·298, ·087; each root not being very different from three times the next after it. I will not go into the affair any further just now. I just wish to call your attention to what Prof. Morley has already done upon the example that I suggested for our arithmetical laboratory. I think it will be worth while also to work out the energy ratios (p. 74). In selecting this example, I designed a case for which the arithmetic would of necessity be highly convergent. But I chose it primarily because it is something like the kind of thing that presents itself in the true molecule:—An elastic complex molecule consisting of a finite number of discontinuous masses elastically connected (with enormous masses in the central parts, that seems certain): the whole embedded in the ether and acted on by the ether in virtue of elastic connections which, unless the molecule were rigid and embedded in the ether simply like a rigid mass embedded in jelly, must consist of elastic bonds analogous to springs.

I think you will be interested in looking at this model which, by the kindness of Prof. Rowland, I am now able to show you.

[In the present article the substance of the lecture is reproduced—with large additions, in which work commenced at the beginning of last year and continued after the lecture, during thirteen months up to the present time, is described—with results confirming the conclusions and largely extending the illustrations which were given in the lecture. I desire to take this opportunity of expressing my obligations to Mr William Anderson, my secretary and assistant, for the mathematical tact and skill, the accuracy of geometrical drawing, and the unfailingly faithful perseverance in the long-continued and varied series of drawings and algebraic and arithmetical calculations, explained in the following pages. The whole of this work, involving the determination of results due to more than five thousand individual impacts, has been performed by Mr Anderson.—K., Feb. 2, 1901.]

§ 1. The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds. I. The first came into existence with the undulatory theory of light, and was dealt with by Fresnel and Dr. Thomas Young; it involved the question, How could the earth move through an elastic solid, such as essentially is the luminiferous ether? II. The second is the Maxwell-Boltzmann doctrine regarding the partition of energy.

§ 2. Cloud I.—Relative Motion of Ether and Ponderable Bodies; such as movable bodies at the earth's surface, stones, metals, liquids, gases; the atmosphere surrounding the earth; the earth itself as a whole; meteorites, the moon, the sun, and other celestial bodies.

§ 1. A crystal in nature is essentially a homogeneous assemblage of equal and similar molecules, which for brevity I shall call crystalline molecules. The crystalline molecule may be the smallest portion which can be taken from the substance without chemical decomposition, that is to say, it may be the group of atoms kept together by chemical affinity, which constitutes what for brevity I shall call the chemical molecule; or it may be a group of two, three, or more of these chemical molecules kept together by cohesive force. In a crystal of tartaric acid the crystalline molecule may be, and it seems to me probably is, the chemical molecule, because if a crystal of tartaric acid is dissolved and recrystallised it always remains dextro-chiral. In a crystal of chlorate of soda, as has been pointed out to me by Sir George Stokes, the crystalline molecule probably consists of a group of two or more of the chemical molecules constituting chlorate of soda, because, as found by Marbach, crystals of the substance are some of them dextro-chiral and some of them levochiral; and if a crystal of either chirality is dissolved the solution shows no chirality in its action on polarised light; but if it is recrystallised the crystals are found to be some of them dextro-chiral and some of them levo-chiral, as shown both by their crystalline forms and by their action on polarised light.