Integrals of the equations of electrodynamics with to the electric constants of a transparent medium

Abstract

Integrals of the equations of propagation of electrical disturbances have been given by the present writer which express the electric and magnetic forces at any point outside a surface enclosing all the sources in terms of an electric current distribution and a magnetic current distribution over the surface. The result for a source at a point can be obtained by taking as the surface a sphere of very small radius with its centre at the point. This suggests that the equations representing Faraday’s laws can be written 1/V 2 ∂X/∂ t +4π i x = ∂ϒ/∂ y – ∂β/∂ z , 1/V 2 ∂X/∂ t + 4π i v =∂∝/∂ z – ∂ϒ/∂ x , 1/V 2 ∂z/∂ t – 4π i z = ∂β/∂ x – ∂∝/∂ y (1) – ∂∝/∂ t + 4π m x = ∂z/∂ y – ∂Y/∂y, – ∂β/∂t + 4π my = ∂X/∂ z – ∂Z/∂ x , – ∂ϒ/∂ t + 4π mz ∂Y/∂ x – ∂X/∂ y , (2) where X, Y, Z are the components of the electric force, α, β, γ are the components of the magnetic force, i x , i y , i z are the components of an electric current distribution, and m x , m y , m z are the components of a magnetic current distribution throughout the space. The object of the present communication is to express X, Y, Z, α, β, γ in terms of the electric current and magnetic current distributions and to apply the result to the discussion of the electric constants of a transparent medium. It is convenient to take instead of equations (1) and (2) the following equations, which include (1) and (2) as a particular case