April 7, 1892 



NATURE 



533 



magnetic actions. M. Poincare appears to think that Mossotti's 

 theory is consistent with and differs but little from Maxwell's. On 

 this Maxwell says (§62):— "The theory of directaction at adistance 

 is mathematically identical with that of action by means of a 

 medium . . . provided suitable hypotheses be introduced when any 

 difficulty occurs. Thus Mossotti has deduced the mathematical 

 theory of dielectrics from the ordinary theory of attraction." 

 Maxwell anyway repudiated Mossotti's theory. M. Poincare 

 introduces a " fluide inducteur" as the name of a thing displaced 

 in the dielectric, when what Maxwell calls electric displacement 

 occurs. This is all very well. It is anyway not inconsistent 

 with Maxwell, even though Maxwell says distinctly that he does 

 not know what the change of structure is like which he calls 

 electric displacement. It might be a bending or twisting or 

 lots of things, but M. Poincare is partially justified in fixing the 

 idea thus. He calls this " fluide inducteur" elastic, though at 

 the same time he calls it incompressible. It is not quite clear 

 what "fluide" means here. M. Poincare certainly observes 

 that the elasticity of the "fluide inducteur" is quite different 

 from that of material bodies, and in fact acknowledges that it is 

 such as can hardly be fairly attributed to an incompressible fluid. 

 Indeed, how can an incompressible fluid be elastic at all? 

 There must be something besides the fluid ; there must be same 

 structure fixed in space which offers an elastic reaction to the 

 fluid when driven past it, or else there must be the two liquids 

 he objects to that are driven past one another. It is hardly a 

 fair representation to talk of an elastic incompressible fluid, and 

 then to invent difficulties', when the phenomena could not con- 

 fessedly he represented by any such thing, but only by a fluid 

 with some other mechanism superadded. 



M. Poincare's statement, "La methode precedente n'est pas 

 la seule que Ton puisse employer pour deduire de la theorie de 

 Maxwell les lois de la distribution electrique," coupled with his 

 further statement of "une autre methode . . . sans supposer 

 I'existence de ce tluide," seems at variance with his implication 

 that this elastic incompressible fluid is part of or involved in 

 Maxwell's theory. 



This leads to the question of how far Mossotti's theory can 

 fairly be considered as a substitution for or as a development of 

 Maxwell's. It does not in any real sense get over action at a 

 distance. There are the honid old electrical charges acting 

 upon one another across a space full of some non-conducting 

 medium. This is practically no advance as far as a theory of 

 electrical action is concerned. It is an advance no doubt as far 

 as the behaviour of the medium is concerned, inasmuch as it 

 enables a time propagation through space to occur ; but as a 

 theory of electric action it is a distinctly retrograde step on 

 Maxwell's scientific position that he did not know what was the 

 structure of the ether. 



M. Poincare proceeds to criticize Faraday's theory of the 

 stresses in the dielectric, which he attributes to Maxwell. He 

 begins by suggesting that the forces should have been explicable 

 by the elasticity of the inductive fluid, in the same way as 

 mechanical forces are due to the elasticity of matter. He 

 has in this quite forgotten that what he calls the elasticity 

 of this fluid, is not a bit like the elasticity of any matter, 

 and would require either a second fluid, which he rejects, 

 or some structure other than the fluid, to explain its pro- 

 perties. Granting such an additional structure, then the elastic 

 energy of the medium, fluid and sttucture combined, does exactly 

 explain the motions of conductors. Nobody has explained 

 exactly ho-^v conductors differ from non-conducting space in 

 structure, and can or do move, and this is not a bit clearer on 

 Mossotti's hypothesis than on any other, not even when the 

 non-conducting diaphragms are made infinitely thin. Maxwell 

 long ago pointed out that no linear system of stress could leave 

 a medium in equilibrium and move bodies immersed in it ; and 

 yet M. Poincare criticizes Faraday's system because it is not 

 linear ; and this after remarking himself that the elasticity pos- 

 tulated already was not a bit like that of matter. All that is 

 necessary is some assumption as to the connection between the 

 conducting matter and the dielectric, for the " fluide inducteur" 

 by hypothesis has elastic properties that make it the seat of the 

 right amount of potential energy ; and all that can possibly be 

 necessary is to connect the matter with it in such a way that the 

 energy of the medium lost when the conductor moves is given 

 up to the conductor. M. Poincare has again omitted to re- 

 member that the peculiar elasticity of the " fluide inducteur " 

 necessitates some structure with which it is connected, and 

 the Faraday stress may be in this structure, and due to its con- 



NO. 1171, VOL. 45] 



nection with the "fluide inducteur," and not at all due to 

 another fluid with peculiar properties. If the stresses are due to 

 the connections of the "fluide inducteur" there is no great 

 difficulty in supposing them proportional to the squares of the 

 displacements of the "fluide inducteur," just as the increased 

 tension of a stretched horizontal string due to a small weight at 

 its centre is proportional to the square of this weight. In fact, 

 a suggested model working upon this sort of principle has been 

 published as illustrating this very point, and Dr. Lodge's model 

 ethers, in the first part of his " Modern Views," are all of this 

 kind. 



M. Poincare proceeds to find "une difficulte plus grave." 

 He creates this by assuming that the energy of the medium is all 

 due to the work done by these mechanical stresses deforming it. 

 This is a most gratuitous assumption. Take the case of the 

 stretched string with the weight on it. The increased energy 

 of the system is not due only to the work done by the increased 

 tension. At last he confesses, however, that if the energy in 

 the dielectric be kinetic and not potential these difficulties would 

 disappear. " Mais on ne peut encore adopter cette interpreta- 

 tion de la pensee de Maxwell sans se heurter a de grandes 

 difficultes." And why? Merely because Maxwell afterwards 

 calls the electric energy potential while he calls the magnetic 

 energy kinetic. Has M. Poincare forgotten that potential 

 energy may in any case be the kinetic energy of an associated 

 system? or can he not imagine two modes of motion of the 

 same medium ? Anyway, if the potential energy may be the 

 kinetic energy of an associated system, and if M. Poincare's 

 difficulties are inapplicable to a kinetic explanation of the 

 phenomena, it se ms impossible but that they are really inapplic- 

 able to a potential system if this system be judiciously devised. 

 It is just here that M. Poincare fails. He revels in elastic fluids, 

 and yet he continually harps upon the same difficulty — namely, 

 "How can an incompressible liquid be elastic at all?" — and 

 instead of once for all solving this by acknowledging that there 

 must be some structure, he reverts to it as if it were a new diffi- 

 culty whenever he comes across its consequences. 



As a mere mathematical work the book is admirable and clear, 

 if a little prolix. Geo. Fras. FitzGerald. 



Trinity College, Dublin, March 24. 



Prof. Burnside's Paper on the Partition of Energy, 

 R.S.E., July 1887. 



In his criticism on a paper of mine on the partition of energy 

 in a set of non-homogeneous spheres (Nature, March 31, p. 

 512), Mr. Watson says that the conclusions are vitiated owing 

 to my having omitted to introduce the frequency factor of 

 collisions before proceeding to take the averages This is not 

 exactly accurate, since a frequency factor is introduced, viz. 

 the relative speed of the centres of inertia of the impinging 

 spheres parallel to the line of impact. 



In the spring of 1888 Prof. Boltzmann published a criticism 

 of the same paper in the Sitzungsberichte oi \.)\q Vienna Academy, 

 in which he contended that the correct frequency factor should 

 be the relative speed of the points of impact of the spheres 

 parallel to the line of impact ; and in which he showed that the 

 result of averaging with this frequency factor is to make the 

 mean rotational energy equal to the mean energy of translation. 

 Had I been entirely satisfied at the time of the cogency of Prof. 

 Boltzmann's reasoning, I should, of course, have published a 

 short note calling attention to the correction he proposed to 

 make ; and I regret now that this was not done, as it would have 

 prevented the waste of a certain amount of valuable time and 

 trouble. W. Burn side. 



Royal Naval College, Greenwich, April i. 



Dr. Watson has shown in his letter to Nature of March 31 

 (p. 512) how the general methods of Maxwell and Boltzmann 

 may be applied to the particular problem discussed by Prof. 

 Burnside. He has also pointed out an error in Burnside's reason- 

 ing — namely, the non-introduction of the factor u - \] + cv, 

 whereby Burnside's conclusions at variance with the Maxwell- 

 Boltzmann law of partition of energy are vitiated. 



You may, perhaps, allow me space to point out a little more 

 precisely in what, as appears to me, the error consists. Burn- 

 side has to find the average value of the expression — 



(« - U + evr) {2w - ^(K + k) [u - U)} 

 (see p. 503). Now, we may take averages in two ways : 



