Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/308

The memoir of 1864 contained an extension of the equations to the case of bodies in motion; the consideration of which naturally revives the question as to whether the aether is in any degree carried along with a body which moves through it. Maxwell did not formulate any express doctrine on this subject; but his custom was to treat matter as if it were merely a modification of the aether, distinguished only by altered values of such constants as the magnetic permeability and the specific inductive capacity; so that his theory may be said to involve the assumption that matter and aether move together. In deriving the equations which are applicable to moving bodies, he made use of Faraday's principle that the electromotive force induced in a body depends only on the relative motion of the body and the lines of magnetic force, whether one or the other is in motion absolutely. From this principle it may be inferred that the equation which determines the electric force^[1] in terms of the potentials, in the case of a body which is moving with velocity w, is

$\mathbf {E} =[\mathbf {w.} \mu \mathbf {H} ]-{\overset {.}{\mathbf {A} }}+\mathrm {grad} \ \psi$.

Maxwell thought that the scalar quantity ψ in this equation represented the electrostatic potential; but the researches of other investigators^[2] have indicated that it represents the sum of the electrostatic potential and the quantity (A.w).

The electromagnetic theory of light was moreover extended in this memoir so as to account for the optical properties of crystals. For this purpose Maxwell assumed that in crystals the values of the coefficients of electric and magnetic induction depend on direction, so that the equation

$\mu \mathbf {H} =\mathrm {curl} \ \mathbf {A}$

is replaced by

$(\mu _{1}H_{x},\mu _{2}H_{y},\mu _{3}H_{z})=\mathrm {curl} \ \mathbf {A}$;

1. It may be here remarked that later writers have distinguished between the electric force in a moving body and the electric force in the aether through which the body is moving, and that E in the present equation corresponds to the former of these vectors.
2. Helmholtz, Journ. für Muth., lxxviii (1874), p. 309; H. W. Watson, Phil. Mag. (6), XIV (1888), p. 271.