Rigorous mathematical formulation of the model of a semi-gray atmosphere in radiative equilibrium

We extend Emden's classical model once more, with the express aim of establishing exact equations, by allowing for the molecular scattering, if only in its simplest isotropic form, of solar radiation. The idea is to include in the elementary model of a semi gray atmosphere, assumed to be in local radiative equilibrium, an element of realism, always trying to keep up analytic tractability as far as possible. The ensuing integral equations will not be solved in the present article, although it will be pointed out that efforts towards their solution are underway, being as they are within the scope of present-day mathematical methods