NA TURE 



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MODERN ELECTRODYNAMICS. 

 Electricite et Optique : la Lumiire et ses Theories 

 Electrodynamiques ; lei^ons pro/essi'es <; la Sorbonnc en 

 1888, 1890 et 1899. Par H. Poincare. Deuxieme 

 edition, revue et completive par J. Blondin et E. 

 Neculcea. Pp. x + 642. (Paris : G. Carre et C. Naud, 

 igoi.) Price Fr. 22. 



IN the present state of electrical and general physical 

 theory there are probably few undertakings more 

 useful towards progress than a critical discussion of the 

 views of other writers by one who has himself thought 

 deeply and read widely on the subject. 



We may recall the stimulus afforded to the progress 

 of Maxwell's electric theory on the Continent by Helm- 

 holtz's early series of critical memoirs (now largely out 

 of date, having served their purpose) that were devoted 

 to the examination of the relation in which that theory 

 stood to the views of electrical action then current. 



The lectures of M. Poincart?, reported and published 

 by his pupils about ten years ago, possessed great in- 

 terest as being an account of the then fresh advances 

 constituted by the experimental investigations of Hertz, 

 from the hand of a writer who occupied one of the 

 highest positions both in the domain of pure mathe- 

 matics and in that of its physical applications. The 

 writer's unlimited command of analysis and the range 

 of his interests were certain to shed new lights on the 

 subject-matter of which he undertook the exposition. A 

 second edition of the ''Electricite et Optique" is now 

 published in a volume of 640 pages, of which about half 

 consists of a report of lectures delivered at the Sorbonne 

 in 1899 on the still more recent improvements of Max- 

 vi'ell's electrodynamic theory which are associated largely 

 with the name of H. A. Lorentz. It is this latter half 

 of the book, giving the writer's reflections and criticisms 

 on a development which is still fresh, that will naturally 

 present the chief interest for others who have meantime 

 been following the progress of the subject. 



The main feature of the new standpoint is the resuscita- 

 tion of the idea of electricity as representing something 

 permanent like matter. In Maxwell's later writings, in 

 which he was mainly occupied in eliminating the hypo- 

 thetical illustrations and models which had guided him 

 to his theory, but were not logically necessary to its 

 formal exposition, there was a tendency for the older idea 

 of an electric charge, as representing something real, to 

 be eliminated. According to his view, the electric current 

 always flows in closed circuits like a current of an in- 

 compressible fluid, so that there is nowhere any tendency 

 to accumulation of electrodynamically effective electricity. 

 It seemed, therefore, possible to do without any intro. 

 duction in detail of an entity whose flow was restricted by 

 the condition that the quantity of it in any given volume 

 could never alter. This conception of circuital electric 

 flow (to use Lord Kelvin's term) required the ascription of 

 properties the same as those of currents to electric excita- 

 tion both in dielectric material substances and in the free 

 Kther itself The displacement current thus introduced 

 is, in fact, the fundamental feature of Maxwell's electro- 

 NO. 1655, VOL. 64] 



dynamics. Its assumption led directly to a simple and 

 perfectly complete theoretical account of the electro- 

 dynamics of material systems at rest, on the basis of laws 

 established long before by Ampere and Faraday ; the appli- 

 cation to bodies in motion was, however, left by Maxwell 

 in an incomplete and tentative state. In 1872, when he 

 published his treatise, the circumstance that the laws of 

 electrolysis imposed the idea that electricity was in some 

 sense or other atomic was definitely realised, but with a 

 certain reluctance ; while in the treatment of bodies in 

 motion the explicit recognition that a moving charge acts 

 as a current had, owing to an oversight arising from his 

 preoccupation with the medium, to be formally introduced 

 into his -equations by Fitzgerald ten years later, though 

 Maxwell fully accepted such action as a fact all the time. 

 This plan of ignoring electricity and treating electro- 

 dynamics on the basis of a uniform medium with physical 

 constants affected by the presence of matter, and sub- 

 jected to various vector disturbances whose nature is 

 unknown, but which are connected by partial differential 

 relations expressing the laws of Amp&re and Faraday, has 

 been very fully developed by Heaviside and by Hertz. 

 In both cases compensation is sought for the variation of 

 the energy of each element of the medium, solely in the 

 work of tractions exerted on its surface by the surround- 

 ing parts. In Heaviside's discussion the problem was 

 treated with great generality and comprehensiveness ; it 

 will suffice here to pass in review the salient features of 

 the more concise analysis advanced by Hertz. The treat- 

 ment of stress by the method of energy requires displace- 

 ment of the medium ; and so the problem of ponderomotive 

 forces becomes related to the general question of moving 

 media, which is the part of the subject that provides the 

 crucial tests of theory. The electromotive phenomena 

 in media at rest are, on the other hand, all involved in 

 the adoption of the aforesaid laws of Ampere and 

 Faraday, as a description of the properties and behaviour 

 of the medium. The same description is extended to 

 media in motion after the manner of Faraday, and the 

 deductive part of the argument is there confined to the 

 determination of the ponderomotive mechanical forces. 

 To obtain them. Hertz subjects his single uniform 

 medium, which he takes to be the seat of the electric 

 and magnetic energy, to static strain without finite 

 motion, and computes the time-rate of alteration of the 

 energies thereby produced in a given element of its mass. 

 He supposes that the polarisations per unit volume, being 

 affections of the medium, are simply convected along 

 with it. If the element of mass were dynamically self- 

 contained and not subject to tractions from the surround- 

 ing parts, its energy would be conserved so that this 

 time-rate of alteration should vanish. As it is, the alter- 

 ation does not vanish, but represents the work done in 

 the element by the tractions acting on its surface. As 

 the element is part of an elastic medium, the work of 

 such surface-tractions ought to be expressible in the form 

 of work of the stress-system, existing in the element, to 

 which these tractions belong. Now the expression for 

 the variation of the energy is thrown by Hertz into the 

 latter form, in fact without the use of any electro- 

 dynamics in the analysis ; and this leads him at once, 

 for the case of isotropic media, to a self-conjugate electro- 

 magnetic stress-system, the same as Maxwell's, as 



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