M. Poincaré and Maxwell

Abstract

IN his recent treatise on “Electricite et Optique,” M. Poincare professes to give a description of Maxwell's theories of electromagnetic 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 direct action at a distance 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 some 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 confessedly be represented by any such thing, but only by a fluid with some other mechanism superadded.