February 19, 1903] 



NA TURE 



3£>3 



abundant attention, it is much to have a method that 

 can deal, in comparative simplicity with edges and 

 prisms and cones. 



The evidence is closing in more and more rigorously 

 that the medium which transmits electrical and radiant 

 effects must either completely accompany matter in bulk 

 in its movements or else be entirely independent of 

 such movements. If we adopt the latter hypothesis, 

 to which theoretical considerations strongly point, and 

 we still consider the aether to be something possessing 

 translatory inertia, the nature of its kinetic energy will 

 be entirely at our disposal as regards interpretation. 



The author's order of exposition, in the theoretical 

 chapters of this book, first develops the equations for 

 the free aether, in terms of a vector potential ; these are 

 naturally purely vibrational ; then the disturbance of 

 electricity, which is really the exciting source of the 

 phenomena, is introduced by adding the electric flux 



-4tr(u, v, ia) to the expression c~ 2 ^(fi G, H), which 



by these equations of propagation is equated to 

 V 2 (F, G, H). In other words, the elements of current 

 are each of them introduced as a simple intrinsic pole of 

 the vector potential, which in other respects obeys the 

 purely vibrational equations for the aether of empty 

 space. These equations, as solved by the Poisson 

 analysis suitable for such cases, represent disturbances 

 travelling out from the poles in the known manner of 

 simple compact propagation, at any rate in all caseswhere 

 the phenomena are periodic. The electric flux thus 

 introduced is here named the convection current, pre- 

 sumably because it is afterwards going to be considered 

 as arising solely from the motion of electric charges or 

 ions ; in the analysis of Appendix C it is the motion of 

 a volume density. The significant remark now follows 

 that 



"the assumption is implicitly involved that Maxwell's 

 aethereal displacement current is independent of the 

 motion of the aether, if there is such a motion." 



Does this mean that it belongs to the aether, but yet 

 is disconnected frorp it so that it is left behind if the 

 aether moves on? One is tempted to amend the last 

 phrase and make it read, " therefore there is no such 

 motion." 



However this may be, practically it comes to the same 

 thing ; in the next chapter, the aethereal part of the 

 total current is taken not to depend on the motion of 

 the aether, but the convection current does depend on the 

 motion of the matter. This leads, as is known, to 

 Fresnel's formula for velocity of optical propagation in 

 moving material media, and to the law of astronomical 

 aberration of light ; and the author's dictum, above 

 quoted, has already postulated that it is not to affect 

 the phenomena whether the aether moves or not. 



The reluctance shown by the author to considering the 

 aether as stationary in space is based mainly, it appears, on 

 the ground that a field of magnetic force must be con- 

 cerned with motion in the aether, so that if that medium 

 were otherwise at rest, waves of radiation would be 

 convected by a magnetic field. This is known not to be 

 the case to any recognisable extent ; and it is here ex- 

 NO. 1738, VOL. 67] 



plained that the magnetic motions are only a part of the 

 disturbance, there being other latent motions in the ajther 

 which may exactly compensate. But, on the other hand, 

 the objection is not essential ; for magnetic energy may 

 not be energy of simple translation, while if it is so, the 

 velocity need not be of detectable magnitude provided 

 the inertia is sufficiently great. And in the latter case 

 these other latent motions would surely be themselves 

 magnetic. This consideration points to retaining the 

 most precise and directly presentable scheme, until it is 

 definitely proved to be too narrow. 



In the body of the book, the mathematical analysis is 

 developed from the foundation of the circuital laws of 

 Ampere and Faraday, as translated into simple analytical 

 form, and rendered self-consistent by the introduction 

 of displacement currents, originally by Maxwell. In 

 Appendix C, these relations are fitted into a purely 

 dynamical frame. They are derived from potential and 

 kinetic energy functions 



W=ij j j(X/+ Yg + Zh)dxdydz; 



but the other Maxwellian expression, more like ordinary 

 kinetic energy, 



is considered to be unwarranted. This must mean that 

 the kinetic energy is distributed in the medium according 

 to the first form of integral, and that the second, though 

 it gives the right total amount throughout all space, does 

 not express its correct distribution in space. This is a 

 question as to matter of fact. Not to press the point 

 that the element of energy given by it is not essentially 

 positive, the first specification might be thought to imply- 

 that (F, G, H) can be expressed in terms of the local 

 conditions alone ; but the only formula for this vector 

 that is given is a volume integral depending on the state 

 of the whole electric field. One result of the change is, 

 of course, that the Poynting vector for the flux of energy 

 must be modified, so that near the vibrator the paths of 

 rays would be altered ; when the waves become plane 

 it does not matter. 



If we turn to the mathematically analogous (but 

 physically different) hydrodynamic theory by way of illus- 

 tration, the kinetic energy of a fluid containing vortex 

 lines can be expressed in terms of the vorticity by a 

 cognate integral involving the vortex distribution alone, 

 and the behaviour of the vortexes might be deduced from 

 it, abstraction being made altogether of the fluid in which 

 they exist. So the phenomena of the electric currents 

 would be developed with abstraction altogether of the 

 aether in which they subsist ; except that, unfortunately, 

 when the field is not steady, all the aether has to be filled 

 with fictitious aethereal current which is not electric flux 

 at all, or else all effects of true electric flux have to 

 be considered as propagated in time. This is, in 

 fact, the course of the actual historical development of 

 the theoretical electrodynamics of ordinary steady 



