Finite Atmospheres with Isotropic Scattering

Some transfer problems in plane parallel atmospheres of finite optical thickness τ₁are considered, the scattering being isotropic with albedo $$\varpi (0 \lt\varpi \leqslant 1$$). The equations for Chandrasekhar's X- and Y-functions are obtained by a simple mathematical method, an extension of one originally due to Ambartsumian. The same method is then used to obtain expressions for the emergent intensities at both faces of the atmosphere when there is thermal emission and when it is subject to incident radiation.