On the radiative equilibrium of a stellar atmosphere. XXIV

Abstract

In this paper the functional equations governing the X- and Y-functions (introduced in Paper XXII) are solved by an iteration process, starting with the "first approximation" X⁽¹⁾=1 and Y⁽¹⁾=e^-τ/μ. The iteration of these functions leads to a "second approximation." The solutions in these approximations are then corrected by a semi-empirical method to satisfy, exactly, an integral property of the X- and Y- functions. It appears that, in this fashion, solutions for the X- and Y-functions, with an error probably not exceeding 1 per cent for τ<0.5, can be found. The construction of standard solutions in conservative cases is also considered. In an appendix (worked jointly with Mrs. Frances H. Breen) tables of the auxiliary functions, for use in conjunction with the exact solutions of Paper XXII, are provided.