July 30, 1891] 



NATURE 



297 



actual or hypothetical matter) say p in number, which 

 has the required values of T and V, and which further 

 gives the same relations of the parameters q, we have 

 obtained a dynamical explanation of the phenomenon. 

 Prof. Poincare remarks with respect to this process that 

 no dynamical solution of the problem obtained in this 

 way can be unique, and that in fact it must be possible to 

 obtain in this way an infinite number of different solu- 

 tions, or to quote his own words : — 



" If any phenomenon admits of a compjete mechanical 

 explanation it will admit of an infinite number of others 

 which equally well account for all the results of experi- 

 ment." 



This, as he reminds us, is confirmed by the history 

 of physical inquiry. Theories inconsistent with one 

 another are elaborated by different persons, and explain 

 the known facts so well that there is hardly anything left 

 to decide which is right. For example, according to 

 Fresnel the direction of vibration in a ray of plane polar- 

 ized light is perpendicular to the plane of polarization, 

 according to Neumann and MacCullagh it is in the 

 plane of polarization. It can hardly be said that any 

 perfectly absolute experimentum crucis has yet been 

 found to decide between these two theories, although 

 the balance of evidence seems decidedly in favour of the 

 view of Fresnel. 



It is, however, to be remembered that while we can 

 find different mechanical theories to explain the facts, the 

 theories are not necessarily distinct ; the mechanism 

 proposed performs functions which must be performed 

 by the actual mechanism whatever that may be. There 

 always is, as the above cited case well illustrates, a unity 

 connecting the different explanations and a consequent 

 element of similarity among them ; and each satisfactory 

 theory elaborated must tend to progress by suggesting 

 modes of deciding in what respects it is redundant or 

 inadequate. 



The difficulty then as to real mechanical explanations 

 of phenomena does not prevent us from making progress 

 in our knowledge of matter. The Lagrangian method, 

 and this is its remarkable merit, enables us to use the 

 parameters instead of the co-ordinates of actual particles, 

 and thereby to predict the existence of further properties 

 of matter capable of throwing light on those already 

 observed. In this way may be lightened the task, hap- 

 pily not likely to be soon relinquished by the human 

 intellect, of inquiring into the actual constitution of 

 matter and the mutual actions of its parts. 



There seems, however, no doubt that Prof. Poincard 

 is correct in his view that the central idea of Maxwell's 

 treatise is to prove the existence of a mechanical explana- 

 tion of electrical phenomena, not indeed actually finding 

 it, but by showing that the Lagrangian method, which 

 presupposes such an explanation, is applicable, and leads 

 to consistent results. 



Coming now to the detailed exposition of Maxwell's 

 theories, the first thing that calls for notice is the theory 

 of electric displacement. This has always been a subject 

 of considerable difficulty. What is electricity ? is it the 

 ether or something in the ether ? in what consists its dis- 

 placement.'' are questions which the anxious inquirer is 

 continually putting, and putting in vain. Maxwell's elec- 

 tric displacement and electric force remain simply ana- 

 logues to the strain and stress in an elastic solid, and it can 

 hardly be said that anyone has yet brought them out of 

 the category of abstractions. No doubt the mechanical 

 analogues suggested by Maxwell himself and by others 

 are helpful in fixing the ideas and enabling the mind to 

 form some concrete conception of what takes place in the 

 medium ; but they may easily be carried too far, and prove 

 the means of leading to error. It is almost better in, 

 some respects to remain content, if possible, with abstrac- 

 tions, until further light as to the properties of the ether 

 is obtained by experiment and observation ; and perhaps 



NO. I 135. VOL. 44] 



it is on this account that Maxwell has abstained from 

 giving such illustrations in his treatise. On the other 

 hand, some notion corresponding to that of electric dis- 

 placement is necessary for any theory of electrical action 

 regarded as propagated through a medium surrounding 

 the electrified bodies, whose charges become thus the 

 surface manifestation of the state of constraint set up in 

 the dielectric by the electrification. 



Prof. Poincard" distinguishes between two fluids — one 

 which he calls electricity, and the other the fltiide induc- 

 teur. Both fluids are incompressible, the latter fills all 

 dielectric space, the former is capable of being produced 

 at or placed at any given place or on any given surface. 

 If, then, within a closed space a quantity of electricity is 

 introduced, as, for example, when a charge is placed on 

 the surface of a conductor, an equal quantity of Xh&jluide 

 inducteur is forced out across the bounding surface. 

 When all the conductors of a system are in the neutral 

 state, iSxcfluide inducteur is in normal equilibrium ; when, 

 on the other hand, the conductors are electrified, the 

 equilibrium ceases to be normal and the state becomes 

 one of constraint. 



There is some advantage in thus distinguishing between 

 the fluid constituting the electrification and that filling 

 the surrounding space, as it; avoids some difficulties of 

 explanation and treatment which arise when only one 

 fluid is considered as producing the phenomena. 



After a rather lengthy but in many points critical 

 exposition of the theory of dielectrics, founded on Poisson's 

 notion of couches de glissevietit, we come to an interest- 

 ing discussion of Maxwell's theory of stresses in a dielec- 

 tric field. By a somewhat different process from that 

 used by Maxwell, the stresses are found for an isotropic 

 field to be a tension along and a pressure across the lines 

 of force of numerical amount KF-ZStt, where K is the 

 specific inductive capacity, and F is the electric force 

 at the point considered. 



On this result Prof. Poincar(f remarks that, although it 

 agrees very well with the observed attractions and repul- 

 sions between electrified bodies, yet if these attractions and 

 repulsions are to be considered as due to the existence of 

 such stresses in an elastic medium, the laws of elasticity 

 for that medium must be very different from those for 

 ordinary substances. The ideas of electric displacement 

 and electromotive force at a point correspond to the 

 strain and stress in an elastic solid ; but, for correspond- 

 ence to stresses of the value F-/87r, it is necessary to find 

 some different forms of displacement or strain than any 

 that have yet been imagined. 



A difficulty here arises to which Poincard attaches 

 considerable importance. The potential energy in the 

 medium is, if/, g, h be the component electric displace- 

 ments, given by the equation 



where dv is an element of volume and the integral is 

 extended through all space. According to Maxwell's 

 hypothesis as to the localization of the energy of the 

 field, the amount contained in an element dv at which 

 the displacements z.xt/,g, h, is 



or Yi.Y'^dvl^iv. Consequently, if F be increased to F -f dY, 

 there will be an increase in the potential energy of 

 amount 2K.Yd¥dvl^TT. If now the stresses act in the 

 medium as ordinary stresses, they must produce corre- 

 sponding strains in each element of volume. Hence if 

 the element dv be a rectangular parallelepiped of edges 

 bx, fiv, bz when the field is free from electric stress, 

 these dimensions will become, when an electromotive 

 force F is produced at the element, respectively 

 bx{i + e-i), by{i-\- e^, bz {i -\- e-^. Hence, if when F 



