A History of the Theories of Aether and Electricity (1910) — part 20 of 29

There is, however, an important difference between the two cases, which was subsequently discussed by W. Thomson, who pursued the analogy in several memoirs.* In order to represent the magnetic field by a conservative dynamical system, we shall suppose that it is produced by a number of rings of perfectly conducting material, in which electric currents are circulating ; the surrounding medium being free aether. Now any perfectly conducting body acts as an impenetrable barrier to lines of magnetic force ; for, as Maxwell showed,f when a perfect con- ductor is placed in a magnetic field, electric currents are induced on its surface in such a way as to make the total magnetic force zero throughout the interior of the conductor.^ Lines of force are thus deflected by the body in the same way as the lines of flow of an incompressible fluid would be deflected by an obstacle of the same form, or as the lines of flow of electric current in a uniform conducting mass would be deflected by the introduction of a body of this form and of infinite resistance. If, then, for simplicity we consider two perfectly conducting rings carrying currents, those lines of force which are initially linked with a ring cannot escape from their entanglement, and new lines cannot become involved in it. This implies that the total number of lines of magnetic force which pass through the aperture of each ring is invariable. If the coefficients of self and mutual induction of the rings are denoted by Z,, Z2, Z12, the electrokinetic energy of the system may be represented by

T = J (Z,*V + 2Z12^ + Z2 v),

where i, i> denote the strengths of the currents; and the condition that the number of lines of force linked with each circuit is to be invariable gives the equations Liii + Z12i2 = constant, Lziz = constant.

• Thomson's Reprint of Papers in Elect, and Mag., §§ 573, 733, 751 (1870- 1872). t Maxwell's Treatise on Elect, and Mag., § 654.

% For this reason "W. Thomson called a perfect conductor nn ideal extreme diamagnetic.

314 Models of the Aether.

It is evident that, when the system is considered from the point of view of general dynamics, the electric currents must be regarded as generalized velocities, and the quantities

(L1i1 + Z,2i2) and (Z12^ + L9i2)

as momenta. The electromagnetic ponderomotive force on the rings tending to increase any coordinate x is dT/dv. In the analogous hydrodynamical system, the fluid velocity corresponds to the magnetic force: and therefore the circulation through each ring (which is defined to be the integral fvds, taken round a path linked once with the ring) corresponds kinematically to the electric current ; and the flux of fluid through each ring corresponds to the number of lines of magnetic force which pass through the aperture of the ring. But in the hydro- dynamical problem the circulations play the part of generalized momenta ; while the fluxes of fluid through the rings play the part of generalized velocities. The kinetic energy may indeed be expressed in the form

where KI, «c2, denote the circulations (so that KI and »c2 are proportional respectively to ^ and 4), and NI, Nn, N2, depend on the positions of the rings ; but this is the Hamiltonian (as opposed to the Lagrangian) form of the energy-function,* and the ponderomotive force on the rings tending to increase any coordinate x is - dK/dx. Since dK/dx is equal to dT/dx, we see that the ponderomotive forces on the rings in any position in the hydrodynamical system are equal, but opposite, to the ponderomotive forces on the rings in the electric system.

The reason for the difference between the two cases may readily be understood. The rings cannot cut through the lines of magnetic force in the one system, but they can cut through the stream-lines in the other : consequently the flux of fluid through the rings is not invariable when the rings are moved, the invariants in the hydrodynamical system being the circulations.

• Cf. Whittaker, Analytical Dynamics, § 109.

Modds of the Aethtr. 315

If a thin ring, for which the circulation is zero, is introduced into the fluid, it will experience no ponderomotive forces ; but if a ring initially carrying no current is introduced into a magnetic field, it will experience ponderomotive forces, owing to the electric currents induced in it by its motion,

Imperfect though the analogy is, it is not without interest. A bar-magnet, being equivalent to a current circulating in a wire wound round it, may be compared (as W. Thomson remarked) to a straight tube immersed in a perfect fluid, the fluid entering at one end and flowing out by the other, so that the particles of fluid follow the lines of magnetic force. If two such tubes are presented with like ends to each other, they attract ; with unlike ends, they repeL The forces are thus diametrically opposite in direction to those of magnets ; but in other respects the laws of mutual action between these tubes and between magnets are precisely the same.*

• The mathematical analysis in this ease is very simple. A narrow rube through which water is flowing may be regarded as equivalent to a source at one end of the tube and a sink at the other; and the problem may therefore be reduced to the consideration of sinks in an unlimited fluid, If there are two sinks in sneh a fluid, of strengths m and */, the Telocity-potential is

at/r + m*//,

where r and i" denote distance from the sinks. The kinetic energy per unit of the fluid is

thedensiryof the fluid; whence it is easily seen that the total energy of the fluid, when the two sinks are at a dtBtance I apart, exceeds the total cneigy when they are at an infinite distance apart by an amount

0iaei+^ld^&m^Mmt1to+k&™l»mat1i> small spheres *, /, surrounding the sinks. By Green's reduces at once to

where the integration is taken over * and «", and m

or »'. The integral taken over *' vanishe

hare

of the fluid is therefore greater when sinks of strengths at, at* are at a

3 1 6 Models of the Aether.

Thomson, moreover, investigated* the ponderomotive forces which act between two solid bodies immersed in a fluid, when one of the bodies is constrained to perform small oscillations. If, for example, a small sphere immersed in an incompressible fluid is compelled to oscillate along the line which joins its centre to that of a much larger sphere, which is free, the free sphere will be attracted if it is denser than the fluid ; while if it is less dense than the fluid, it will be repelled or attracted according as the ratio of its distance from the vibrator to its radius is greater or less than a certain quantity depending on the ratio of its density to the density of the fluid. Systems of this kind were afterwards extensively investigated by C. A. Bjerknes.f Bjerknes showed that two spheres which are immersed in an incompressible fluid, and which pulsate (i.e., change in volume) regularly, exert on each other (by the mediation of the fluid) an attraction, determined by the inverse square law, if the pulsations are concordant ; and exert on each other a repulsion, determined likewise by the inverse square law, if the phases of the pulsations differ by half a period. It is necessary to suppose that the medium is incom- pressible, so that all pulsations are propagated instantaneously : otherwise attractions would change to repulsions and vice versa at distances greater than a quarter wave-length.^ If the spheres, instead of pulsating, oscillate to and fro in straight lines about their mean positions, the forces between them are proportional in magnitude and the same in direction, but

mutual distance I than when sinks of the same strengths are at infinite distance apart by an amount lirpmm'/l. Since, in the case of the tubes, the quantities m correspond to the fluxes of fluid, this expression corresponds to the Lagrangian form of the kinetic energy ; and therefore the force tending to increase the coordi- nate x of one of the sinks is (3/9#) (4ny> ww'/Z). "Whence it is seen that the like ends of two tubes attract, and the unlike ends repel, according to the inverse square la\r.

• Phil. Mag. xli (1870), p. 427.

t Repertorium d. Mathematik von Konisberger und Zeuner (1876), p. 268. Gottinger Nachrichten, 1876, p. 245. Comptes Rendus, Ixxxiv (1877), p. 1377. Cf. Nature, xxiv (1881), p. 360.

J On the mathematical theory of the force between two pulsating spheres in a fluid, cf. W. M. Hicks, Proc. Camb. Phil. Soc. iii (1879), p. 276 ; iv (1880), p. 29.

Models of the Aether. 3 1 7

opposite in sign, to those which act between two magnets oriented along the directions of oscillation.*

The results obtained by Bjerknes were extended by A. H. Leahyf to the case of two spheres pulsating in an elastic medium ; the wave-length of the disturbance being supposed large in comparison with the distance between the spheres. For this system Bjerknes' results are reversed, the law being now that of attraction in the case of unlike phases, and of repulsion in the case of like phases : the intensity is as before proportional to the inverse square of the distance.

The same author afterwards discussed \ the oscillations which may be produced in an elastic medium by the displacement, in the direction of the tangent to the cross- section, of the surfaces of tubes of small sectional area : the tubes either forming closed curves, or extending inde- finitely in both directions. The direction and circumstances of the motion are in general analogous to ordinary vortex- motions in an incompressible fluid ; and it was shown by Leahy that, if the period of the oscillation be such that the waves produced are long compared with ordinary finite distances, the displacement due to the tangential disturbances is proportional to the velocity due to vortex-rings of the same form as the tubular surfaces. One of these " oscillatory twists," as the tubular surfaces may be called, produces a displacement which is analogous to the magnetic force due to a current flowing in a curve coincident with the tube ; the strength of the current being proportional to b'w sin pt, where b denotes the radius of the twist, and t» sin pt its angular displacement. If the field of vibration is explored by a rectilineal twist of the same period as that of the vibration, the twist will experience a force

• A theory of gravitation has heen hased by Korn on the assumption that gravitating particles resemhle slightly compressible spheres immersed in an incom- pressible perfect fluid : the spheres execute pulsations, whose intensity corresponds to the mass of the gravitating particles, and thus forces of the Newtonian kind are produced between them. Cf. Korn, Eine Theorie der Gravitation und der elect. Etscheinungen, Berlin, 1898.

t Trans. Camb. Phil. Soc. xiv (1884), p. 45.

J Trans. Camb. Phil. Soc. xiv (1885), p. 188.

3 1 8 Models of the Aether.

at right angles to the plane containing the twist and the direction of the displacement which would exist if the twist were removed ; if the displacement of the medium be repre- sented by F sin pt, and the angular displacement of the twist by w sin pt, the magnitude of the force is proportional to the vector-product of V (in the direction of the displacement) and w (in the direction of the axis of the twist).

A model of magnetic action may evidently be constructed on the basis of these results. A bar-magnet must be regarded as vibrating tangentially, the direction of vibration being parallel to the axis of the body. A cylindrical body carrying a current will have its surface also vibrating tangentially ; but in this case the direction of vibration will be perpendicular to the axis of the cylinder. A statically electrified body, on the other hand, may, as follows from the same author's earlier work, be regarded as analogous to a body whose surface vibrates in the normal direction.

We have now discussed models in which the magnetic force is represented as the velocity in a liquid, and others in which it is represented as the displacement in an elastic solid. Some years before the date of Leahy's memoir, George Francis Fitz Gerald (b. 1851, d. 1901)* had instituted a comparison between magnetic force and the velocity in a quasi-elastic solid of the type first devised by MacCullagh.f An analogy is at once evident when it is noticed that the electromagnetic equation

4?rD = curl H is satisfied identically by the values

4?rD = curl e, H = e,

where e denotes any vector; and that, on substituting these values in the other electromagnetic equation,

• curl (4ircsD/e) - H, •

• Phil. Trans., 1880, p. 691 (presented October, 1878). Fitz Gerald's Scientific Writings, p. 45. t Cf. p. 155.

Moaeh of the Aether. 319

we obtain the equation

ee + c2 curl curl e = 0,

which is no other than the equation of motion of MacCullagh's aether,* the specific inductive capacity £ corresponding to the reciprocal of MacCullagh's constant of elasticity. In the analogy thus constituted, electric displacement corresponds to the twist of the elements of volume of the aether ; and electric charge must evidently be represented as an intrinsic rotational strain. Mechanical models of the electromagnetic field, based on Fitz Gerald's analogy, were afterwards studied by A. Sommerfeld,f by K. Keiff,J and by Sir J. Larmor.§ The last-named authorll supposed the electric charge to exist in the form of discrete electrons, for the creation of which he suggested the following ideal processIF : — A filament of aether, terminating at two nuclei, is supposed to be removed, and circulatory motion is imparted to the walls of the channel so formed, at each point of its length, so as to produce throughout the medium a rotational strain. When this has been accomplished, the channel is to be filled up again with aether, which is to be made continuous with its walls. When the constraint is removed from the walls of the channel, the circulation imposed on them proceeds to undo itself, until this tendency is balanced by the elastic resistance of the aether with which the channel has been filled up ; thus finally the system assumes a state of equilibrium in which the nuclei, which correspond to a positive and a negative electron, are surrounded by intrinsic rotational strain.

Models in which magnetic force is represented by the velocity of an aether are not, however, secure from objection. It is necessary to suppose that the aether is capable of flowing like a perfect fluid in irrotational motion (which would corre-

• Cf. p. 155. t Ann. d. Phys. xlvi (1892), p. 139.

I Reiff, Elasticitat und Elektricitdt, Freiburg, 1893. § Phil. Trans, clxxxv (1893), p. 719.

|| In a supplement, of date August, 1894, to his above-cited memoir of 1893. H Phil. Trans, clxxxv (1894), p. 810; cxc (1897), p. 210; Larmor, Aether .and Matter (1900), p. 326.

320 Models of the Aether.

spond to a steady magnetic field), and that it is at the same time endowed with the power (which is requisite for the explanation of electric phenomena) of resisting the rotation of any element of volume.* But when the aether moves irrota- tionally in the fashion which corresponds to a steady magnetic field, each element of volume acquires after a finite time a rotatory displacement from its original orientation, in con- sequence of the motion ; and it might therefore be expected that the quasi-elastic power of resisting rotation would be called into play — i.e., that a steady magnetic field would develop electric phenomena.f

A further objection to all models in which magnetic force corresponds to velocity is that a strong magnetic field, being in such models represented by a steady drift of the aether, might be expected to influence the velocity of propagation of light. The existence of such an effect appears, however, to be disproved by the experiments of Sir Oliver Lodge ; J at any rate, unless it is assumed that the aether has an inertia at least of the same order of magnitude as that of ponderable matter, in which case the motion might be too slow to be measurable.

Again, the evidence in favour of the rotatory as opposed to the linear character of magnetic phenomena has perhaps, on the whole, been strengthened since Thomson originally based his conclusion on the magnetic rotation of light. This brings us to the consideration of an experimental discovery.

In 1879 E. H. Hall,§ at that time a student at Baltimore,

• Larmor (loc. cit.) suggested the analogy of a liquid filled with magnetic molecules under the action of an external magnetic field.

It has often heen objected to the mathematical conception of a perfect fluid that it contains no safeguard against slipping between adjacent layers, so that there is no justification for the usual assumption that the motion of <i perfect fluid is continuous. Larmor remarked that a rotational elasticity, such as is attributed to the medium above considered, furnishes precisely such a safeguard ; and that without some property of this kind a continuous frictionless fluid cannot be imagined.

t Larmor proposed to avoid this by assuming that the rotation which is resisted by an element of volume of the aether is the vector sum of the series of differential rotations which it has experienced. J Phil. Trans, clxxxix (1897), p. 149.

§ Am. Jour. Math, ii, p. 287 ; Am. J. Sci. xix, p. 200, and xx, p. 161 ; Phil. Mag. ix, p. 225, and x, p. 301.

Models of the Aether. 321

repeating an experiment which had been previously suggested by H. A. Kowland, obtained a new action of a magnetic field on electric currents. A strip of gold leaf mounted on glass, forming part of an electric circuit through which a current was passing, was placed between the poles of an electro- magnet, the plane of the strip being perpendicular to the lines of magnetic force. The two poles of a sensitive galvano- meter were then placed in connexion with different parts of the strip, until two points at the same potential were found. When the magnetic field was created or destroyed, a deflection of the galvanometer needle was observed, indicating a change in the relative potential of the two poles. It was thus shown that the magnetic field produces in the strip of gold leaf a new electromotive force, at right angles to the primary electromotive force and to the magnetic force, and proportional to the product of these forces.

From the physical point of view we may therefore regard Hall's effect as an additional electromotive force generated by the action of the magnetic field on the current ; or alternatively we may regard it as a modification of the ohmic resistance of the metal, such as would be produced if the molecules of the metal assumed a helicoidal structure about the lines of magnetic force. From the latter point of view, all that is needed is to modify Ohm's law

S = £E

(where S denotes electric current, k specific conductivity, and E electric force) so that it takes the form

S = KE + h [E . H]

where H denotes the imposed magnetic force, and h denotes a constant on which the magnitude of Hall's phenomenon depends. It is a curious circumstance that the occurrence, in the case of magnetized bodies, of an additional term in Ohm's law, formed from a vector-product of E, had been expressly suggested in Maxwell's Treatise*: although Maxwell had not- indicated the possibility of realizing it by Hall's experiment.

• Elect, and Mag., § 303. Cf. Hopkinson, Phil. Mag. x (1880), p. 430.

Y

322 Models of the Aether.

An interesting application of Hall's discovery was made in the same year by Boltzmann,* who remarked that it offered a prospect of determining the absolute velocity of the electric charges which carry the current in the strip. For if it is supposed that only one kind (vitreous or resinous) of electricity is in motion, the force on one of the charges tending to drive it to one side of the strip will be proportional to the vector- product of its velocity and the magnetic intensity. Assuming that Hall's phenomenon is a consequence of this tendency of charges to move to one side of the strip, it is evident that the velocity in question must be proportional to the magnitude of the Hall electromotive force due to a unit magnetic field. On the basis of this reasoning, A. von Ettingshausenf found for the current sent by one or two Daniell's cells through a gold strip a velocity of the order of 0*1 cm. per second. It is clear, however, that, if the current consists of both vitreous and resinous charges in motion in opposite directions, Boltzmann's argument fails ; for the two kinds of electricity would give opposite directions to the current in Hall's phenomenon.

In the year following his discovery, Hall} extended his researches in another direction, by investigating whether a magnetic field disturbs the distribution of equipotential lines in a dielectric which is in an electric field ; but no effect could be observed.§ Such an effect, indeed,|| was not to be expected on theoretical grounds; for when, in a material system, all the velocities are reversed, the motion is reversed, it being understood that, in the application of this theorem to electrical theory, an electrostatic state is to be regarded as one of rest, and a current as a phenomenon of motion ; and if such a reversal be

• Wien Anz., 1880, p. 12. Phil. Mag. ix (1880), p. 307.

t Ann. d. Phys. xi (1880), pp. 432, 1044.

1 Am. Jour. Sci. xx (1880), p. 164.

§ In 1885-6 E. van Aubel, Bull, de 1'Acad. Roy. de Belgique (3) x, p. 609 ; xii, p. 280, repeated the investigation in an improved form, and confirmed the result that a magnetic field has no influence on the electrostatic polarization of dielectrics.

|| H. A. Lorentz, Arch. Neerl. xix (1884), p. 123.

Models of the Aether. 323

performed in the present system, the poles of the electro- magnet are exchanged, while in the dielectric no change takes place.

We must now consider the bearing of Hall's effect on the question as to whether magnetism is a rotatory or a linear phenomenon.* If magnetism be linear, electric currents must be rotatory; and if Hall's phenomenon be supposed to take place in a horizontal strip of metal, the magnetic force being directed vertically upwards, and the primary current flowing horizontally from north to south, the only geometrical entities involved are the vertical direction and a rotation in the east- and-west vertical plane ; and these are indifferent with respect to a rotation in the nor th-and- south vertical plane, so that there is nothing in the physical circumstances of the system to determine in which direction the secondary current shall flow. The hypothesis that magnetism is linear appears therefore to be inconsistent with the existence of Hall's effect, f There are, however, some considerations which may be urged on the other side. Hall's effect, like the magnetic rotation of light, takes place only in ponderable bodies, not in free aether ; and its direction is sometimes in one sense, sometimes in the other, according to the nature of the substance. It may therefore be doubted whether these phenomena are not of a secondary character, and the argument based on them invalid. Moreover, as Fitz Gerald remarked,^ the magnetic lines of force associated with a system of currents are circuital and have no open ends, making it difficult to imagine how alteration of rotation inside them could be produced.

Of the various attempts to represent electric and magnetic phenomena by the motions and strains of a continuous medium, none of those hitherto considered has been found free from

• Of. F. Kol&cek, Ann. d. Phys. Iv (1895), p. 503.

t Further evidence in favour of the hypothesis that it is the electric phenomena which are linear is furnished by the fact that pyro-electric effects (the production of electric polarization by warming) occur in acentric crystals, and only in such. Cf. M. Abraham, Encyklopiidie der rnrith. Wiss. iv (2), p. 43.

I Cf. Larmor, Phil. Trans, clxxxv, p. 780.

Y 2

324 Models of the Aether.

objection.* Before proceeding to consider models which are not constituted by a continuous medium, mention must be made of a suggestion offered by Biemann in his lecturesf of 1861. Rie- mann remarked that the scalar-potential 0 and vector-potential a, corresponding to his own law of force between electrons, satisfy the equation

0 + div a = 0 ;

an equation which, as we have seen, is satisfied also by the potentials of L. Lorenz.j This appeared to Riemann to indicate that <j> might represent the density of an aether, of which a represents the velocity. It will be observed that on this hypothesis the electric and magnetic forces correspond to second derivates of the displacement — a circumstance which makes it somewhat difficult to assimilate the energy possessed by the electromagnetic field to the energy of the model.

We must now proceed to consider those models in which the aether is represented as composed of more than one kind of constituent : of these Maxwell's model of 1861-2, formed of vortices and rolling particles, may be taken as the type. Another device of the same class was described in 1885 by Fitz Gerald§ ; this was constituted of a number of wheels, free to rotate on axes fixed perpendicularly in a plane board ; the axes were fixed at the intersections of two systems of perpendicular lines ; and each wheel was geared to each of its four neighbours by an indiarubber band. Thus all the wheels could rotate without any straining of the system, provided they all had the same angular velocity; but if some of the wheels were revolving faster than others, the indiarubber bands would become strained. It is evident that the wheels in this model play the same part as the vortices in Maxwell's model of 1861-2 : their rotation is

• Cf. H. "Witte, Ueber den gegenwdrtigen Stand der Frage nach einer mecha- nischen Erkldrung der elektrischen Erscheinungen ; Berlin, 1906.

t Edited after his death by K. Hattendorff, under the title Schwere, Elektricitiit, und Magnetismus, 1875, p. 330.

I Cf. p. 299.

§ Scient. Proc. Koy. Dublin Soc., 1885; Phil. Mag. June, 1885; Fitz Gerald's Seient. Writings, pp. 142, 157.

^B Models of the Aether. 325

the analogue of magnetic force ; and a region in which the masses of the wheels are large corresponds to a region of high magnetic permeability. The indiarubber bands of Fitz Gerald's model correspond to the medium in which Maxwell's vortices were embedded ; and a strain on the bands represents dielectric polari- zation, the line joining the tight and slack sides of any band being the direction of displacement. A body whose specific inductive capacity is large would be represented by a region in which the elasticity of the bands is feeble. Lastly, conduction may be represented by a slipping of the bands on the wheels.

Such a model is capable of transmitting vibrations analogous to those of light. For if any group of wheels be suddenly set in rotation, those in the neighbourhood will be prevented by their inertia from immediately sharing in the motion; but presently the rotation will be communicated to the adjacent wheels, which will transmit it to their neighbours; and so a wave of motion will be propagated through the medium. The motion constituting the wave is readily seen to be directed in the plane of the wave, i.e. the vibration is transverse. The axes of rotation of the wheels are at right angles to the direction of propagation of the wave, and the direction of polarization of the bands is at right angles to both these directions.

The elastic bands may be replaced by lines of governor balls :* if this be done, the energy of the system is entirely of the kinetic type.f

Models of types different from the foregoing have been suggested by the researches of Helmholtz and W. Thomson on vortex-motion. The earliest attempts in this direction, however, were intended to illustrate the properties of ponderable matter rather than of the luminiferous medium. A vortex existing in a perfect fluid preserves its individuality throughout all changes,

• Fitz Gerald's Scient. Writings, p. 271.

t It is of course possible to devise models of this class in which the rotation may be interpreted as having the electric instead of the magnetic character. Such a model was proposed by Boltzinann, Vorlesungen iiber Maxwell's Theorie, ii.

326 Models of the Aetker.

and cannot be destroyed ; so that if, as Thomson* suggested in 1867, the atoms of matter are constituted of vortex-rings in a perfect fluid, the conservation of matter may be immediately explained. The mutual interactions of atoms may be illustrated by the behaviour of smoke-rings, which after approaching each other closely are observed to rebound : and the spectroscopic properties of matter may be referred to the possession by vortex-rings of free periods of vibration. f

There are, however, objections to the hypothesis of vortex- atoms. It is not easy to understand how the large density of ponderable matter as compared with aether is to be explained ; and further, the virtual inertia of a vortex-ring increases as its energy increases ; whereas the inertia of a ponderable body is, so far as is known, unaffected by changes of temperature. It is, moreover, doubtful whether vortex-atoms would be stable. " It now seems to me certain," wrote W. Thomson^ (Kelvin) in 1905, " that if any motion be given within a finite portion of an infinite incompressible liquid, originally at rest, its fate is necessarily dissipation to infinite distances with infinitely small velocities everywhere; while the total kinetic energy remains constant. After many years of failure to prove that the motion in the ordinary Helmholtz circular ring is stable, I came to the conclusion that it is essentially unstable, and that its fate must be to become dissipated as now described."

The vortex-atom hypothesis is not the only way in which the theory of vortex-motion has been applied to the construc- tion of models of the aether. It was shown in 1880 by W. Thomson§ that in certain circumstances a mass of fluid can exist in a state in which portions in rotational and irrotational

• Phil. Mag. xxxiv(1867), p. 15; Proc. R.S. Edinb. vi, p. 94.

t An attempt was made in 1883 by J. J. Thomson, Phil. Mag. xv (1883), p. 427, to explain the phenomena of the electric discharge through gases in terms of tho theory of vortex-atoms. The electric field was supposed to consist in a distribution of velocity in the medium whose vortex-motion constituted the atoms of the gas ; and Thomson considered the effect of this field on the dissociation and recoupling of vortex-rings.

J Proc. Roy. Soc. Edinb., xxv (1905), p. 565.

§ Brit. Assoc. Rep., 1880, p. 473.

Models of the Aether. 327

motion are finely mixed together, so that on a large scale the mass is homogeneous, having within any sensible volume an equal amount of vortex-motion in all directions. To a fluid having such a type of motion he gave the name vortex-sponge.

TiveTyears later, Fitzgerald*" discussed the suitability of the vortex-sponge as a model of the aether. Since vorticity in a perfect fluid cannot be created or destroyed, the modification of the system which is to be analogous to an electric field must be a polarized state of the vortex motion, and light must be represented by a communication of this polarized motion from one part of the medium to another. Many distinct types of polarization may readily be imagined : for instance, if the turbulent motion were constituted of vortex-rings, these might be in motion parallel to definite lines or planes ; or if it were constituted of long vortex filaments, the filaments might be bent spirally about axes parallel to a given direction. The energy of any polarized state of vortex-motion would be greater than that of the unpolarized state; so that if the motion of matter had the effect of reducing the polarization, there would be forces tending to produce that motion. Since the forces due to a small vortex vary inversely as a high power of the distance from it, it seems probable that in the case of two infinite planes, separated by a region of polarized vortex-motion, the forces due to the polarization between the planes would depend on the polarization, but not on the mutual distance of the planes — a property which is characteristic of plane distributions whose elements attract according to the Newtonian law.

It is possible to conceive polarized forms of vortex- motion which are steady so far as the interior of the medium is concerned, but which tend to yield up their energy in producing motion of its boundary — a property parallel to that of the aether, which, though itself in equilibrium, tends to move objects immersed in it.

In the same year Hicksf discussed the possibility of trans-

• Scient. Proc. Roy. Dublin Soc., 188o • Scientific Wntings of FitzGerakl, p. 154. + Brit. Assoc. Rep., 1885, p. 930.

328 Models of the Aether.

mitting waves through a medium consisting of an incompressible fluid in which small vortex-rings are closely packed together. The wave-length of the disturbance was supposed large in com- parison with the dimensions and mutual distances of the rings ; and the translatory motion of the latter was supposed to be so slow that very many waves can pass over any one before it has much changed its position. Such a medium would probably act as a fluid for larger motions. The vibration in the wave- front might be either swinging oscillations of a ring about a diameter, or transverse vibrations of the ring, or apertural vibrations ; vibrations normal to the plane of the ring appear to be impossible. Hicks determined in each case the velocity of translation, in terms of the radius of the rings, the distance of their planes, and their cyclic constant.