An extension of the findings of RM-4651-NASA on the absorption of photons incident to an atmosphere, to the case of an inhomogeneous atmosphere and anisotropic scattering. By use of the invariant imbedding technique, two complete sets of integro-differential equations are derived--the first for the case of monodirectional illumination of the upper boundary, and the second for monodirectional illumination of the lower boundary--using the equations of transfer and taking into account the polarity of the optical properties of the atmosphere. In both sets, the equations and results for scattering and transmission in the homogeneous case reduce to those given by Chandrasekhar. 30 pp. Ref.