Electromagnetic potentials in a heterogeneous non-conducting medium

For electromagnetic fields in a stationary non-conducting medium (isotropic or anisotropic), whose dielectric constant and permeability are given point-functions, the general theory of representations in terms of scalar and vector potentials and of Hertzian potentials is developed. Differential equations relating these potentials to the sources of the field are obtained. Special cases are also treated of representations in terms of two scalars satisfying second-order differential equations. This paper contrasts with a recent alternative approach (Nisbet 1955a), in which the properties of the medium were introduced through the electric and magnetic polarizations rather than the dielectric constant and permeability, and which led to integro-differential equations.