On the radiative equilibrium of a stellar atmosphere. II

In this paper a new method is described for solving the various problems of radiative transfer in the theory of stellar atmospheres. The basic idea consists in expressing the integral (proportional to the density of radiation) which occurs in the equation of transfer as a sum according to Gauss's formula for numerical quadratures and replacing the integrodifferential equation by a system of linear equations. General solutions of this linear system can readily be written down, and this enables one to obtain solutions for the various problems to any desired degree of accuracy. The method has been applied in detail to the problem considered in the earlier paper, and the first four approximations explicitly found. The corresponding laws of darkening have also been determined. An interesting by-product of the investigation is a new and entirely elementary proof of the exact Hopf Bronstein relation, giving the boundary temperature in terms of the effective temperature