September 12, 1895] 



NA TURE 



475 



Phil. Mag., October 1887, p. 342) at the Manchester meeting 

 ■discussed the question much more thoroughly and satisfactorily, 

 and deduced that the velocity a', propagation was V^/i times 

 the velocity of mean square of the turbulent motion. We can 

 make little further progress until we Unow something of the 

 arrangement of the small motions which confer the quasi- 

 rigidity. This may be completely irregular and unsteady, or 

 arranged in some definite order of steady motions. I am in- 

 clined to the view that the latter is nearer the truth. In this 

 case we should expect a regular structure of small cells in which 

 the motions arc all similar. By the word cell I do not mean a 

 small vessel bounded by walls, but a portion of the fluid in 

 which the motion is a complete system in itself. Such a theory 

 might be called a cell theorj- of the ether. The simplest type, 

 perhaps, is to suppose the medium spaced into rectangular 

 boxes, in each of which the motion may be specified as follows : 

 Holding the box with one set of faces horizontal the fluid streams 

 up in the centre of the box, then turns round, flows down the 

 sides and up the centre again. In fact, it behaves like a Hill's 

 vortex squeezed from a spherical into a box form. Each box 

 has thus rotational circulation complete in itself. The six ad- 

 joining compartments have their motion the same in kind, but 

 in the reverse direction, and so on. In this way we get con- 

 tinuous and energetic small motions throughout the medium, 

 and the state is a stable one. If there is a shear, so that each 

 cell becomes slightly rhomboidal, the rotational motions inside 

 lend to- prevent it, and thus propagate the disturbance, but the 

 cells produce no effect on the general irrotational motion of the 

 fluid, at least when the irrotational velocities are small compared 

 with those of the propagation of light. In this case the rate at 

 which the cells adjust themselves to an equilibrium position is 

 far quicker than the rate at which this equilibrium distribution 

 «s disturbed by the gross motions. The linear dimensions of the 

 cells must be small compared with the wave-lengths of light. 

 They must probably be small also compared with the atoms of 

 gross matter, which are themselves small compared with the 

 same standard. 



We may regard each cell as a djTiamical system by itself, into 

 which we pour or take away energy. This added energy will 

 depend only on the shape into which the box is deformed. We 

 may then, for our convenience in considering the gross motions 

 of the medium as a whole, i.e. our secondary medium, regard 

 these as interlocked .systems, neglect the direct consideration of 

 Ihc motions inside them, but regard the energy which they 

 absorb as a potential function for the general motion. This 

 jiotential function will contain terms of two kinds, one involving 

 the shear of the cells, and this shear will be the santc as the 

 rotational deformation in the secondary medium. The second 

 will depend on alterations in the ratios of the edges of the cells 

 (including other changes of form involving no rotations). The 

 former will give rise to waves of transversal displacements. The 

 second cannot be transmitted as waves, btu may i>roduce local 

 cftects. If a continuous solid be placed in such a medium, the cells 

 will rearrange themselves so as to keep the continuity of their 

 motions. The cells will become distorted (but without resultant 

 shear), and a static stress will be set up. We have then to deal 

 with the primary stuff' itself, whose rotation gives a structure 

 to the ether, and the structural ether itself. The form-;r 

 we may call the primary medium. The ether which can 

 transmit transversal disturb.ances, and which is built up out of 

 the first, we may call the secondary medium. Whether an atom 

 of matter is to he considered as a vortical mass of the primary 

 or of the secondary medium is a matter to be left open in the 

 jjresent state of the theory. 



At the Bath meeting of this A.ssociation, I sketched out a 

 theory of the electrical action of a fluid ether in which electrical 

 lines of force were vortex filaments combined with an equivalent 

 number of hollow vortices of the same vortical strength. (" A 

 Vortex Analogue of .Static I'.lectricity," Brit. Assoi. Kcp., 1888, 

 p. 577.) An electric charge on a body depended on the number 

 of ends of filaments abutting on it, the sign being determined 

 by the direction of rotation of the filament looked at from the 

 body. This theory gave a complete account of electrostatic 

 actions, both quantitatively and qualitatively, and a more specu- 

 lative one as to currents and magneti.sm. I could only succeed 

 in proving at that lime that if the filaments were distributed 

 according to the .same laws as electric lines of force, the distri- 

 bution would be one of equilibrium. Larmor ("A Dynamical 

 Theory of the Electric and Luminiferous Medium," Phil. Trans., 

 4894, p. 748) has recently proved that this is also the necessary 



NO. 1350, VOL. 52] 



distribution for any type of a rotationally elastic ether, and con- 

 sequently also for this particular case. Currents along a wire 

 were supposed to consist of the ends of filaments running along 

 it, with disappearance of the hollow companions, the filaments 

 producing at the same time a circulation round the wire. A 

 magnetic field was thus to be produced by a flow of the ether, 

 but probably with the necessary accompaniment of rotational 

 elements in it. 



This latter, however, w;is clearly wrong, because each kind of 

 filament would produce a circulation in opposite directions. The 

 correct deduction would have been to lay stress on the fact that 

 the field is due to the motion through the stationary ether of the 

 vortex filaments, the field being perpendicular to the filament 

 and to its direction of motion. This motion would doubtless 

 produce stresses in the cell-ether due to deformations of the cells, 

 and be the proximate cause of the mechanical forces in the field. 

 In any case, it is not difficult to show that a magnetic field can- 

 not be due to an irrotational flow of. the ether alone.' Such 

 electrostatic and magnetic fields produce states of motion in the 

 medium, but no bodily flow in it ; consequently we ought not 

 to expect an effect to be produced on the velocity of transmis- 

 sion of light through it. 



The fundamental postulate underlying this explanation of 

 electric action is that when two different kinds of matter are 

 brought into contact a distribution of vortex filaments in the 

 neighbourhood takes place, so that a larger number stretch from 

 one to the other than in the opposite direction — the distinction 

 between positive and negative ends being that already indicated. 

 To see how such a distribution may be caused, let us consider 

 each vortex atom to be composed of a vortical mass of our 

 secondary medium or cell-structure ether. The atom is much 

 larger than a cell, and contains practically an infinite number of 

 them. It is a dynamical system of these cells with equilibrium 

 of energy throughout its volume. The second atom is a dy- 

 namical system w ith a different equilibrium of energy. \\Tiere 

 they come into contact there will be a certain surface rearrange- 

 ment, which w ill show itself as a surface distribution of energy 

 in a similar manner to that which exists between a molar collec- 

 tion of one kind of molecules in contact w ith one of another, 

 and which shows itself in the phenomenon which we call surface 

 tension. In the present case the effect may take place at the 

 interface of two atomic .systems in actual contact, or be a differ- 

 ence effect between the two interfaces of the ether and each 

 atom when the latter are sufficiently close. The surface effect 

 \\e are now- considering shows itself as contact electricity. 



Such a distribution of small vortex filaments, stretching from 

 one 'atom to another, will tend to hold them together. We 

 therefore get an additional cause for aggregation of atoms. This 

 does not exclude the others already referred to. They may all 

 act concurrently, some producing one effect, .some another — one 

 combining, perhaps, unknown primitive atoms into elements, 

 one elements into chemical compounds, and another producing 

 the cohesion t>f matter into masses. 



On this theory the difference between a conductor and a 

 dielectric is that in a dielectric the ends of the filaments cannot 

 pass from atom to atom, possibly because the latter never come 

 into actual contact. In a conductor, however, we are to suppose 

 that the atomic elements can do so. WTien a current is flowing, 

 a filament and its equivalent hollow stretch between two 

 neighbouring atoms, they are pulled into contact, or their 

 motions bring them into contact, the hollow disappears, and the 

 rotational filament joins its two ends and sails away as a small 

 neutral vortex ring into the surrounding medium, or returns to 

 its function as an ether cell. The atoms being free are now 

 pulled back to perform a similar operation for other filaments. 

 The result is that the atoms are set into violent vibrations, 

 causing the heating of the conductor. When, however, the 

 metal is at absolute zero of temperature, there is no motion, the 

 atoms are already in contact, and there is no resistance, as the 

 observation of Dewar and Fleming tends to show. Further, as 

 the resistance depends on the communication of motion from 

 molecule to molecule, we should expect the electrical conduc- 



l To prove this, consider a straight conductor moving parallel to itself 

 and perpendicular to a uniform magnetic tield. There e.Msrs a permanent 

 potential difference between its ends. I f, however, the field consists of a flow 

 of ether, the effect is the same .xs if the conductor is at re-st, and the direc- 

 tion of the magnetic tleld shifted ihrouyh an angle. But this is the case of 

 a conductor at rest in .1 field, and there is therefore no potential (iifference 

 between the ends. Hence a magnetic field must consist of some structure 

 across which the conductor cuts A field m.iy possibly demand a flow of 

 the ether, but, if so, it must carry in it some structure defiiiitely oriented 

 at each point to the direction of flow. 



