On the Radiative Equilibrium of a Stellar Atmosphere. VII.

In this paper the problem of the radiative equilibrium of a stellar atmosphere in local thermody- namic equilibrium is reconsidered with a view to examining in detail the effects of a continuous absorp- tion coefficient, K~, dependent on frequency. It is shown that when the material departs from gray- ness the corrections which have to be made to the temperature distribution are of two kinds: first, because the integrated Planck intensity B is not, in general, equal to the average integrated intensity J (= S SI4wdv/4-n-) and, second, because the energy density of the radiation does not have the gray atmospheric value. To evaluate the corrections arising from these two sources, a systematic method of approximation has been developed in which the first approximation is assumed to be given by the solu- tion for a gray atmosphere with a !C~ equal to a ;ertain appropriately chosen mean absorption coefficient ;~. It is found that the best way of choosing ~ is to define it as a straight mean of icr, weighted according to the net monochromatic flux F~1) (r) of radiation of frequency v in a gray atmosphere