n 



262 



NATURE 



[January 1 1, 1894 



our continuous analysis is not any longer applicable to the pro- 

 blem of reflexion ; the condiiions at the interface are altogether 

 too numerous to be satisfied by the available variables. There 

 is in fact discontinuity at the interface in the discrete molecular 

 structure, such as could not be representable by a continuous 

 analysis. But if we proceed by the method of rays, and assume 

 that there is a play of surface forces which do not absorb any 

 energy, while they adjust the dispersional part of the stress, it 

 appears that reflexion is independent of dispersion. 



The problem of the aether has been first determinedly attacked 

 from the side of electrical phenomena by Clerk Maxwell in 

 quite recent times ; his great memoir on a " Dynamical Theory 

 of the Electromagnetic Field " is of date 1864. It is in fact 

 only comparatively recently that the observation of Oersted, 

 • and the discoveries and deductions of Ampere, Faraday, and 

 Thomson had accumulated sufficient material to allow the 

 question to be profitably attacked from this side. Even as it is, 

 our notions of what constitute electric and magnetic phenomena 

 are of the vaguest as compared with our ideas of what consti- 

 tutes radiation, so that Maxwell's views involve difficulties, not 

 to say contradictions, and in places present obstacles which are 

 to be surmounted, not by logical argument or any clear repre- 

 sentation, but by the physical intuition of a mind saturated with 

 this aspect of the phenomena. Many of these obstacles may, I 

 think, be removed by beginning at the other end, by explaining 

 electric actions on the Imsis of a mechanical theory of radiation, 

 instead of radiation on the basis ot electric actions. The strong 

 pomt of Maxwell's theory is the electromotive part, which gives 

 an account of electric radiation and of the phenomena of 

 electromagnetic induction in fixed conductors; and this is in 

 keeping with the remark just made. The nature of electric 

 displacement, of electric and magnetic forces on matter, of 

 what Maxwell calls the electrostatic and the magnetic stress in 

 the medium, of electrochemical phenomena, are all left 

 obscure. 



We shall plunge into the subject at once from the optical 

 side, if we assume that dielectric polarisation consists in a strain 

 in the aether, of the rotational character conteiuplaied above 

 The conditions of internal equilibrium of a medium so straine't 

 are easily worked out from MacCullagh's expression for W, 

 its potential energy. If the vector (/, g, h) denote ihe curl or 

 vorticity of the actual linear displacement of the medmm, or 

 twice the absolute rotation of the portion of the medium at the 

 point considered, and the medium is supposed of crystalline 

 quality and referred to its principal axes, so that 



W = i /" («-/- -t- b^-g"^ + cVC) dr, 



where dr is an element of volume, it follows easily that for in- 

 ternal equilibrium we must have 



ar/dx + b-g dy + c"h dz ■=. —dV, 



a complete differential, and that over any boundary enclosing a 

 region devoid of elasticity the value of V must be constant. 

 Such a boundary is the surface of a conductor ; V is the elec- 

 tric potential in the field due to charges on the conductors ; 

 {/, g, h) is the electric displacement in the field, circuital by its 

 very nature as a rotation, and {a-f, b'^g, c'-h) is the electric 

 force derived from the electric poiential V. The charge on a 

 conductor is the integral of (f, g, h) over ary surface enclosing 

 it, and cannot be altered except by opening u^) a ch;innel devoid 

 of elasticity, in the medium, between ihis conductor ani some 

 other one ; in other words, electric discharge can take place 

 only by rupture of the elastic quality of the setherial n.ediuni. 



At the imerlace between two dielecitic media, taken to lie 

 crystalline as above, the condition comes out 10 be thai the 

 tnngential electric force is continuous. When the circum-tances 

 are those of equilibrium, and therefore an electric (joiemial 

 may be introduced, this condition allows discontilaJit^ in ihe 

 value of the potential in crossing the interface, but demanils 

 that the amount of this discontinuity shall be ihe same all 

 along ihe interface ; these are precisely the circumstances o the 

 observed phenomena of voltaic polen'ial differences. The com- 

 ponent, no mal to ihe interface, of the eleciiic di-pl icemen' is 

 of course aUays continuous, from the nature "f that vector as 

 a flux. 



It may present itself as a difificuliy in this theory that, as the 

 electric displacement is the rotational .li^,.lacement of the 

 medium, its surface integral over any sheet should be equal to 



NO. 1263, VOL. 4q] 



the line integral of the linear displacement of the medium 

 round the edge of the sheet ; therefore that for a closed sheet 

 surrounding a conductor this integral should be null, which 

 would involve the consequence that the electric charge on a 

 conductor cannot be different from null. This line of argument, 

 however, implies that the linear displacement is a perfectly con- 

 tinuous one, which is concomitant with and required by the 

 electric displacement. The legitimate inference is that the 

 electric displacement in the medium which corresponds to an 

 actual charge cannot be set up without some kind of discontin- 

 uity or slip m the linear displacement of the medium ; in other 

 words, that a conductor cannot receive an electric charge with- 

 out rupture of the surrounding medium ; nor can it lose a 

 charge once received without a similar rupture. The part of 

 the linear displacement that remains, after this slip or rupture 

 has been deducted from it, is of elastic origin, and must satisfy 

 the equations of equilibrium of the medium. 



Wc can produce in imagination a steady electric current, 

 without introducing the complication of galvanic batteries, in 

 the following manner, and thus examine in detail all that is 

 involved, on the present theory, in the notion of a current. 

 Suppose we have two charged condensers, with one pair of 

 coatings connected by a narrow conducting channel, and 

 the other pair connected by another such channel, as in 

 the annexed diagram, where the dark regions are dielectric 



and the white regions conducting. If we steadily move 

 towards each other the two plates of the condenser A, a 

 current will flow round the circuit, in the form of a con- 

 duction current in the conductors and a displacement 

 current across the dielectric plates of the condensers. Let 

 us suppose the thicknesses of these dielectric plates to be 

 excessively small, so as to minimise the importance of the dis- 

 placement part of the current. There is then practically no 

 electric force and therefore no electric displacement in the 

 surrounding dielectric field, except between the plates of the 

 condensers and close to the conducting wires. Consider a closed 

 surface passing between the faces of the condenser A, and inter- 

 secting the wire at a place P. A movement of the faces of this 

 condenser alters the e'ectric force between them, and therefore 

 alters the electric displacement across the portion of this closed 

 surface which lies in that part of the field ; as we have seen, 

 there is practically no displacement anywhere else in the field 

 except at the conducting wire ; therefore to preserve the law of 

 the circuital character of dis|>lacement throughout the whole 

 spare, we must suppose that this alteration is comiensaled by a 

 ve^ V iiiten^e change of displacement at the conducting wire. So 

 long as the movement of the plates continues, as long does this 

 fl w of displacement along the wire go on ; it cons' itutes the 

 eleciiic current in the wire. Now, in calculatint; the magnetic 

 force in ihe field, which is the velocity of the seiheieal medium, 

 from the change of electric displacement, we mus' include in 

 <.u integration the effect of this sheet of electric di-|Iacement 

 flowing along the surface of the perfectly conducting wires, for 

 exactly the same reason as in the correlative problem in hydro- 

 d}namics, of calculating the velocity of the fluid from the dis- 

 tribution of vorticity in it, Helmholtz had to consider a vortex 

 sheet as existing over each surface across which the motion is 

 discontinuous. 



{To be continued.) 



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