2/4 



NATURE 



[July i8, 1901 



providing the reacting mechanical forces required for 

 equilibration of the outstanding energy. But for 

 a^olotropic media there arises a bodily torque in addition 

 to this stress ; this torque is included in Maxwell's 

 general type of magnetic stress, and prevents it from 

 being self-conjugate for that case. Hertz is unwilling to 

 admit such a type of stress, which could not e.\ist in an 

 ordinary elastic solid ; but he is at a loss to know what 

 to do with this new part, and simply drops it, retaining 

 the self-conjugate part as the stress in his electric 

 medium. But for this the theory would be a consistent 

 one on his premisses ; and the result for the free aether, or 

 wherever there is no material polarisation, is, in fact, the 

 stress which Maxwell showed was competent to represent 

 the actual mechanical forces. It is to be observed that 

 this is all that is to be got out of the statical application 

 of the principle of energy to his medium ; the kinetics 

 of the electromotive play being assumed as known, out- 

 standing variations of the energy in slow changes are to 

 be ascribed to the work of mechanical forces. No 

 success has been achieved in the problem of reducing 

 the electromotive play in media in motion to definite self- 

 contained dynamics on any other basis than (he theory 

 of electrons ; the charge must consist of discrete in- 

 dependent elements, each with its own electric field. 

 The mode of treatment here sketched introduces, among 

 other things, a mechanical force of an electric field on 

 changing magnetic polarisation as the counterpart of the 

 known mechanical force of a magnetic field on changing 

 electric polarisation ; this, on the theory of electrons, is 

 non-existent. 



The treatment of electrodynamics on the basis of 

 discrete electrons is a branch of statistical molecular 

 theory, like the kinetic theory of gases, and involves the 

 refined considerations connected therewith, including the 

 estimation of averages instead of the following out of 

 individuals. The care that is thus necessary in the 

 analysis may be illustrated by a temporary slip that has 

 crept in at the beginning of the discussion of Lorentz's 

 theory (§ 333), in which the single principle of continuity 

 of flux of true electricity appears as a consequence of 

 the addition of two independent formulas, (3) and (4), 

 neither of which appears again. They cannot be both 

 true, or there would be two such principles of continuity 

 instead of one. It would seem that the term density has 

 been inadvertently used in two different senses, ultimately 

 as the volume density of electric charge in the medium 

 which depends on how closely the electrons are packed in 

 it, but meanwhile as the density of electricity in an electron, 

 supposed to be itself a small and rigid though mobile 

 volume-distribution of charge. This local oversight, doubt- 

 less due to imperfect reporting of the lectures, illustrates 

 an actual disadvantage of a completed hypothesis, which 

 insists on a full specification of an electron, over the less 

 complete physical specification, which, recognising that 

 there is more in the constitution of the molecule of matter 

 than our philosophy may ever reach, is content to regard 

 it simply as the unknown central point or pole of its 

 surrounding field of force. 



The general plan of development of electrodynamics 



on this basis that is adopted by M. Poincare consists in 



writing clown equations of motion for each electron, by 



assigning to it a mass and considering it to be acted on 



NO. 1655, VOL. 64] 



by the averaged or smoothed-out electric and magnetic 

 forces of the field that surrounds it, and finally passing 

 to equations for the medium in bulk by summing or 

 averaging the results for all the electrons per unit volume. 

 This method is in keeping with the astronomical tradi- 

 tions of mathematical physics, in which the problem is 

 put in definite terms at the beginning, and the analysis 

 is confined to surmounting the difiiculties, purely mathe- 

 matical, that arise in its unravelment. There is, how- 

 ever, a different kind of theoretical physics which has 

 had more success in this country, which recalls the 

 names of Young, Stokes, Kelvin and Maxwell, and has 

 more recently in Germany been illuminated by the ex- 

 ample and inspiration of Helmholtz. Care is taken 

 to avoid an irrevocable formulation of the problem in 

 advance, only its broad dynamical features being 

 worked in ; while all the light that cognate but better 

 understood branches of physics can shed by way of 

 illustration or analogy is pressed into service. Thus, 

 instead of writing out isolated equations of motion for 

 the ideal case of a single electron — on the tacit assump- 

 tion that no other electrons are near which would disturb 

 the averaged field that is alone supposed to affect it— it 

 is recognised that electrons, possibly in very large 

 number, are somehow involved in the structure of each 

 individual molecule, and that the fundamental and 

 essential clement in the physics of matter in bulk is 

 this permanent molecule considered as a single free 

 vibrating system, with free periods producing a radiant 

 spectrum, which are involved in the intrinsic mutual 

 influence of these oscillating electrons. The simplest 

 type of framework for the structure of such a system is 

 to assume provisionally a gyrostatic orbital constitution 

 of some kind, which assists in holding its parts together 

 in some such way as the whirling motion holds together 

 a vortex ring in fluid. Our dynamical plan is thus now 

 no longer fi.xed, but flexible ; in fact it must remain so 

 until we can form a definite representation of such a 

 molecule instead of only a general idea of it. Yet the 

 uniformity of physical law for matter in bulk shows that 

 we ought to be able to develop our synthesis without 

 waiting for such knowledge, which may even quite pos- 

 sibly be unattainable. In this procedure we must attend 

 primal ily to such activities of the molecules as can be 

 cumulated by addition, so as to produce aggregate results 

 expressible per unit volume of the medium, and eliminate 

 the remaining non-cumulative disturbance which is 

 related to practically irreversible or thermal phenomena. 

 Of the former class is the strain in the configuration of 

 the molecule produced by the electric or magnetic field 

 in which it is situated, this distortion being represented 

 for statical purposes by a single vector quantity, the 

 induced electric or magnetic moment of the molecule, 

 which aggregates into induced polarity of the material 

 medium. Such, also, are the types and energies of free 

 vibration about the steady configuration, which have 

 been analysed in their aggregate into definite periods 

 by the spectroscope. Here our knowledge is related to 

 general principles rather than special systems, and pro- 

 gress is possible, thanks to the purely abstract general 

 formulation of dynamics by Lagrange and Hamilton, 

 and also to the supports and signposts afforded by such 

 phenomena as anomalous optical dispersion and the 



