§ 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.

The presence of helium in the residue after removal of nitrogen from this gas was proved in a former paper, but there was some doubt as to the relative proportions of argon and helium. A fresh sample, kindly collected by Dr Richardson, has therefore been examined. Of this 2,500 c.c., submitted to electric sparks in presence of oxygen, gave a final residue of 37 c.c., after removal of all gases known until recently. The spectrum of the residue, observed at atmospheric pressure, showed argon, and the D3 line of helium very plainly.

The easy visibility of D3 suggested the presence of helium in some such proportion as 10 per cent., and this conjecture has been confirmed by a determination of the refractivity of the mixture. It may be remembered that while the refractivity of argon approaches closely that of air, the relative number being 0·961, the refractivity of helium (as supplied to me by Professor Ramsay) is very low, being only 0·146 on the same scale. If we assume that any sample of gas is a mixture of these two, its refractivity will determine the proportions in which the components are present.

The observations were made by an apparatus similar in character to that already described, but designed to work with smaller quantities of gas.

On a recent occasion I remarked that Stewart's work appeared to me to be insufficiently recognized upon the Continent. One reason for this is probably the comparative inaccessibility of the Edinburgh Transactions in which his first paper appeared. Another may be found in the fact that the paper itself is not well arranged, and that the principal conclusion is put forward in the first instance as if it were the result of Stewart's special experiments. The experiments were indeed of great value; but this course gave an opening to Kirchhoff's objection that “this proof [of the law that the absorption of a plate equals its radiation and that for every description of heat] cannot be a strict one, because experiments which have only taught us concerning more and less, cannot strictly teach us concerning equality.” I am inclined to think that Stewart would have received more recognition if he had never experimented at all!

While yielding to no one in admiration for Kirchhoff, I can hardly regard him as in this matter an impartial critic. In a paper which should be studied by the historical inquirer, Stewart himself protests against some of Kirchhoff's remarks, and to my judgment makes out his case. In his excellent Handbuch der Spectroscopie, recently published, Prof. Kayser, with evident desire to be impartial, gives Stewart much, but not all, of the credit that I would claim for him.

As some recent viva voce remarks of mine have received an interpretation more wide than I intended, I shall be glad to be allowed to explain that when (now several years ago) I became acquainted with the work of van t' Hoff I was soon convinced of the great importance of the advances due to him and his followers. The subject has been prejudiced by a good deal of careless phraseology, and this is probably the reason why some distinguished physicists and chemists have refused their adhesion. It must be admitted, further, that the arguments of van t' Hoff are often insufficiently set out, and are accordingly difficult to follow. Perhaps this remark applies especially to his treatment of the central theorem, viz. the identification of the osmotic pressure of a dissolved gas with the pressure which would be exercised by the gas alone if it occupied the same total volume in the absence of the solvent. From this follows the formal extension of Avogadro's law to the osmotic pressure of dissolved gases, and thence by a natural hypothesis to the osmotic pressure of other dissolved substances, even although they may not be capable of existing in the gaseous condition. If I suggest a somewhat modified treatment, it is not that I see any unsoundness in van t' Hoff's argument, but because of the importance of regarding a matter of this kind from various points of view.

In a paper published sixteen years ago I drew attention to a peculiarity of the magnetic rotation of the plane of polarisation arising from the circumstance that the rotation is in the same absolute direction whichever way the light may be travelling. “A consequence remarkable from the theoretical point of view is the possibility of an arrangement by which the otherwise general optical law of reciprocity shall be violated. Consider, for example, a column of diamagnetic medium exposed to such a force that the rotation is 45°, and situated between two Nicols whose principal planes are inclined to one another at 45°. Under these circumstances light passing one way is completely stopped by the second Nicol, but light passing the other way is completely transmitted. A source of light at one point A would thus be visible at a second point B, when a source at B would be invisible at A; a state of things at first sight inconsistent with the second law of thermodynamics.” (Phil. Trans. CLXXVI. p. 343, 1885; Scientific Papers, Vol. II. p. 360.) It is here implied that the inconsistency is apparent only, but I did not discuss it further.

In his excellent report (“Les Lois théoriques du Rayonnement, Rapports présentés au Congrès International de Physique,” Paris, 1900, Vol. II. p. 29), W. Wien, considering the same experimental combination of Nicols and magnetised dielectric, arrives at a contrary conclusion. It may be well to quote his statement of the case.

The subject under discussion includes both natural and artificial flight. Although we are familiar with the flight of birds, there are many interesting questions which arise in connexion with natural flight, and some of them are yet very obscure.

In still air a bird, being heavier than the fluid displaced, cannot maintain his level for more than a short time without working his wings. In this matter the vicarious principle holds good. If the bird is not to fall, something must fall instead of him, and this can only be air. The maintenance of the bird thus implies the perpetual formation of a downward current of air, and involves therefore performance of work. Later we shall consider more particularly how this work is applied; but a preliminary difficulty remains to be discussed. It is well known that large birds, such as vultures and pelicans, are often observed to maintain their level for considerable periods of time, without flapping or visibly working their wings. On a smaller scale, and in more special situations, sea-gulls in these latitudes perform similar feats. This question of the soaring or sailing flight of birds has given rise to much difference of opinion. Few of the naturalists, to whom we owe the observations, are familiar with mechanical principles, and thus statements are often put forward which amount to mechanical impossibilities.