Page:Aether and Matter, 1900.djvu/25

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CONTENTS
xix
Page


Chapter VI Dynamical theory of electrical actions 82
Least Action, fundamental in general dynamics. Dynamical equations for free aether, derived from its energy function: the two fundamental vectors, circuitally related: velocity of elastic propagation. Introduction of electrons, as point-charges. Modification of relation of aethereal strain to displacement in a medium containing electrons: displacement of an electron equivalent to a local aether strain: two independent variables, electric flux and aether strain: combined they form Maxwell's circuital total current. Generalization of Stokes' theorem of circuit and barrier integration, for a medium containing singularities. In ordinary electrodynamics, aether strain inconsiderable compared with electric flux: expression of the kinetic energy of the aether in terms of electric flux, viz. in terms of true flux of electrons and 'apparent' flux the equivalent of change of aether-strain, involves the introduction of the vector potential of the electric flux: the potential energy involves the aether strain alone. Application of Action principle to the energy as thus specified: introduction of the additional condition that each electron is a pole of the aether strain: variation performed as regards a moving electron: interpretation of result as giving the electric force acting on the electrons and the aethereal force straining the aether: modification required in magnetized media to obtain the 'mechanical' part of the electric force which excludes the purely local part: the mechanical force on an electric current. Electric currents of conduction, due to motions of ions, constituted half by positive and half by negative ions. Currents producing material electric polarization. Current arising from convection of charged bodies. Current arising from convection of a polarized dielectric, expressible primarily as a quasi-magnetization. Any magnetization identical mechanically with a distribution of current. Total mechanical force on the material medium, as constituted by the force on the true current, that on the magnetism, that on the electric polarization and the true electric charge: the part of it arising from the convection of the medium. The vector potential of magnetism must be defined as that of the equivalent distribution of electric flow: this equivalence extends to magnetic induction, not to magnetic force.
Chapter VII Review of the electrodynamic equations of a material medium 109
Exact dynamical relations. Exact relations inherent in the constitution of the medium. Consequences: the static electric force due to the actual distribution adds to the kinetically induced force. Approximate constitutive relations of the material medium: dielectric and magnetic coefficients: analysis of aeolotropic conduction, any rotational character must De due to extraneous vector influence. Elimination of mathematical potentials: the circuital relations. Maxwell's purely abstract scheme; determinate for media at rest and
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