Joseph Larmor

“ The aim of a theory of the æther is not the impossible one of setting down a system of properties in which everything that may hereafter be discovered in physics shall be virtually included, but rather the practical one of simplifying and grouping relations and of reconciling apparent discrepancies in existing knowledge. ”

“ Although the Gaussian aspect of the subject, which would simply assert that the primary atoms of matter exert actions on each other which are transmitted in time across space in accordance with Maxwell's equations, is a formally sufficient basis on which to construct physical theory, yet the question whether we can form a valid conception of a medium which is the seat of this transmission is of fundamental philosophical interest, quite independently of the fact that in default of the analogy at any rate of such a medium this theory would be too difficult for development. ”

“ Further, since rotation of the body without deformation cannot alter the potential energy of mutual configuration of the molecules, it follows that for a rectangular element of ordinary solid matter the tangential components of these tractions must be self-conjugate, as they are taken to be in the ordinary theory of elasticity. On the other hand, for a medium not molecularly constituted we can hardly treat at all of mutual configuration of parts, and the self-conjugate stress-relation will not be a necessary one. ”

“ A medium, in order to be available at all, must transmit actions across it in time ; therefore there must be postulated for it the property of inertia, — of the same kind as ordinary matter possesses, for there can hardly be a more general kind, — and also the property of elasticity or statical resistance to change either of position or of form. In ordinary matter the elasticity has reference solely to deformation; while in the constitution here assumed for the æther there is perfect fluidity as regards form, but elastic resistance to rotational displacement. ”

“ The point of view has been enlarged: the ordinary notion of the transmission of force, as framed mathematically by Lagrange and Green for a simple elastic medium without singularities, is not wide enough to cover the phenomena of a medium containing intrinsic strain-centres which can move about independently of the substance of the medium. But the same mathematical principles lead to the necessary extension of the theory, when the energy function thus involves the positions of the strain-centres as well as the elastic displacement in the medium ”

“ As a gas at high temperature must contain molecules with all amounts of internal thermal energy from nothing upwards, we should on the other hand, on the ordinary gas-theory, expect both a shift of the brightest part of a spectral line when the temperature is raised, and also a widening of its diffuse margin. ”

“ In the Faraday-Maxwell theory, however, as usually expounded, an explanation of these equations is found, explicitly or tacitly, in an assumption that the æther is itself polarizable in the same manner as a material medium, and æther is in fact virtually considered to be matter; on the present theory the equations for free space are an analytical statement of the ultimate dynamical definition of the continuous æthereal medium, and the polarization of material bodies with the resulting forcive are deduced from the relation of their molecules to this medium in which they have their being. ”

“ To derive the play of internal force, this energy function must be varied with respect to all these independent quantities; the result is elastic tractional stress in the medium across every ideal interface, together with forcive tending to displace each strain-centre, which we can consider either as resisted by extraneous constraint preventing displacement of the strain-centre, or as compensated by the reaction of the inertia of the strain-form against acceleration. ”

“ The objection that rotational elasticity postulates absolute directions in space need hardly have weight when it is considered that a definite space, or spacial framework fixed or moving, to which motion is referred, is a necessary part of any dynamical theory. ”

“ Discussions as to transmission by contact are not the fundamental ones, as the above actual material illustration shows: the single comprehensive basis of dynamics into which all such partial modes of explanation and representation must fit and be coordinated is the formula of Stationary Action, including, as the particular case which covers all the domain of steady systems, the law that the mutual forces of such a system are derived from a single analytical function which is its available potential energy. ”

“ The elastic and other characteristics of ordinary matter, including its viscous relations, are on the other hand a direct consequence of its molecular constitution, in combination with the law of material energy which is itself a consequence of the fact that the energies of the atoms are wholly located in the surrounding simple continuous æther and are thus functions of their mutual configurations. ”

“ According to the present scheme the ponderomotive forces acting on matter arise from the forces acting on the electrons which it involves; the application of the principle of virtual work to the expression for the strain-energy shows that, for each electron at rest, this force is equal to its charge multiplied by the intensity of the electric field where it is situated. ”

“ The potential energy, from which the forces are derived, is a function of the mutual configurations of the parts of the material system. In the case of forces of elasticity the internal energy is primarily a function of the mutual configurations of the individual molecules, from which a regular or organised part (§ 49 infra) is separated which is expressible in terms of the change of configuration of the differential element of volume containing a great number of molecules, and from which alone is derived the stress that is mechanically transmitted. ”

“ It is only in electromagnetic phenomena and molecular theory that non-vibrational movements of the æther are involved. The æther not being matter, it need not obey the laws of the dynamics of matter, provided it obey another scheme of dynamical laws consistent among themselves; these laws must however be such that we can construct in the æther an atomic system of matter which itself obeys the actual material laws. ”

“ The transmission of material traction by an ordinary solid, which is now often taken as the type to which all physical action must conform, is merely an undeveloped notion arising from experience, which must itself be analysed before it becomes of scientific value: the explanation thereof is the quantitative development of the notion from the energy function by the method of virtual work in the manner indicated in § 10 infra. ”

“ A theory which, like the present one, explains atoms of matter as made up of singularities of strain and motion in the æther, is bound to look for an explanation of gravitation by means of the properties of that medium ”

“ Such constraints as may be necessary to prevent division of their vacuous nuclei are outside our present scope; and mutual destruction of two complementary electrons by direct impact is an occurrence of infinitely small probability. The model of an electron thus formed will persist for any finite assignable time if the distribution of gyrostatic momentum in the medium is sufficiently intense: but the constitution of our model of the medium itself of course prevents, in this respect also, absolute permanence. ”

“ Across an interface the traction in the tether must be continuous, so that the tangential component of the æthereal force (P', Q', R') must be continuous, which is satisfied by continuity of Ψ. The continuity of the total electric current secures itself without further condition by a compensating distribution of electric charge on the interface, that is by a discontinuity in dΨ/dn. The tangential continuity of the elastic æther requires that the tangential component of the magnetic force (α, β, γ) must be continuous ”

“ When a conducting system is in steady motion so that there is no conduction current flowing into it, the electric force (P, Q, R) must be null throughout its substance. Thus for the case of a solid conductor rotating round an axis of symmetry in a uniform magnetic field parallel to that axis, with steady angular velocity ω, the electric force in it, namely , must be null, so that ; the polarization in it is therefore null, but there is in it an æthereal displacement . ”

“ But though that philosophy has abundantly vindicated itself as regards the secondary properties of matter, which are amenable to direct examination, its rigid application would debar us from any theory of the æther at all, as we can only learn about it from circumstantial evidence. ”

“ The present view requires that the energy of chemical constitution shall be very great compared with the thermal energy; but for this very reason our means of chemical decomposition are limited, so that only a part of that energy is experimentally realizable. ”

“ The æther is a perfect fluid endowed with rotational elasticity; so in the first place we have — and this is the most difficult part of our undertaking — to construct a material model of a perfect fluid, which is a type of medium nowhere existing in the material world. ”

“ The translatory motions of the molecules would diminish without limit, and therefore also the opportunities for reaction between them, so that many chemical changes would cease to take place for the same reason that a fire ceases to burn when the supply of air is insufficient, or coal gas ceases to explode when too much diluted with air: but the energies of affinity exist all the time in probably undiminished strength, while the forces of cohesion are modified by the fall of temperature but not necessarily in the direction of extinction. ”

“ In Rankine's special and peculiar imagery, the æther was however a polar medium or system (as contrasted with a body) made up of polarized nuclei (Cf. Part I., §§ 37-8) whose vertical atmospheres, where such exist, constitute material atoms. The supposed necessity of having the vibration at right angles to the plane of polarization also misled him to the introduction of complications into the optical theory, such as æolotropic inertia, and to deviations from MacCullagh's rigorous scheme.↑ The use of these studs is to maintain continuity of motion of the medium without the aid of viscosity ”

“ We may imagine that neither of them has any internal heat; so that the internal energy of each is the minimum that corresponds to its steady gyrostatic momentum, and the axis of each gyrostat therefore keeps a fixed direction in space. The result of the encounter will be that the axis of each gyrostat acquires steady wobbling or free processional motion, so that its internal energy is increased at the expense of the energy of translation of the atoms ”

“ In outside space, the electric force and æthereal force are each , where Ψ2 is that free electrostatic potential which is continuous with the surface value at the conductor. Inside the conductor this purely æthereal displacement involves an electrification of volume density , which will be a density of free electrons or ions as all true electrifications are ”

“ It therefore cannot represent directly, after the manner of a stress across a medium, a force acting on matter, for that would from this ultimate standpoint be a force acting on a strain-form spreading from its nucleus all through the medium, not a traction on a definite surface bounding the matter. ”

“ This stress, between two molecules, is usually sensible only at molecular range; hence the action of the surrounding parts on a portion of a solid body is practically made up of tractions exerted over the interface between them. ”

“ The position that we are concerned in supporting is that the cosmical theory which is used in the present memoirs as a descriptive basis for ultimate physical discussions is a consistent and thinkable scheme ”

“ If however there are also other types of momenta associated with the atom, for example if the case of the gyrostat is not massless, the encounter will leave vibrations about the new state of steady motion, which if of high enough period will lead to loss of energy by radiation.↑ Ideas somewhat similar to the above are advanced by Waterston in his classical memoir of 1845 on gas-theory, recently edited by Lord Rayleigh ”

“ If this distinction did not exist, both conduction and convection must ultimately depend on transfer by ordinary radiation at small distances, as Fourier imagined; and it would not appear why convection by a gas, even when highly rarefied, is so much more efficient in the transfer of heat than radiation. ”

“ The circumstance that no mode of transmission of the mechanical forces, of the type of ordinary stress across the æther, can be put in evidence, thus does not derogate from the sufficiency of the present standpoint. ”

“ In this way the purely a priori standpoint is pushed away a stage, and we may find justification against the reproach that a philosophical formulation of dynamics should be concerned only with relative motions. ”