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Phys. (USSR) 8 , 6 5 (1944). [Astrophysics 7. V. V. SOBOLEV, O n certain functions in the theory o f light scattering, Astrofiz. 3 , 4 3 3 (1967) 3 , 205 (1967)]. 8. I. N . M I N I N , A . G . P I L I P O S Y A N a n d N . A . S H I D L O V S K A Y A , T a b l e s o f t h e A m b a r t s u m y a n f u n c t i o n s f o r anisotropic scattering, Trudy Astron. Obs. Leningrad Gos. Univ. 2 0 (1963). Leningrad 9. I. N . M I N I N , Diffuse reflection f r o m a semi-infinite m e d i u m for anisotropic scattering.

V . V . SOBOLEV, A n i s o t r o p i c scattering o f light in a semi-infinite atmosphere. I, Astron. Zh. 4 5 , 2 5 4 (1968) [Sov. J. 1 2 , 2 0 2 (1968)]. 13. H . C . V A N D E H U L S T , High-order scattering in diffuse reflection from a semi-infinite atmosphere, Astronomy and Astrophysics 9 , 374 (1971). Chapter 3 ATMOSPHERES OF FINITE OPTICAL THICKNESS I N THIS chapter we shall examine the problem o diffu se reflection and transmission of light by an atmosphere of finite optical thickness r 0.

We begin with the basic integral equation for the source function B(t, rj, £). 34) for m = 0. 67). 96) where C is some constant. For the determination of C we use the following approach. 92) in order to apply it to the deep layers of the medium. 4). 92) and using the superposition theorem for solutions of linear equations, we find B(%, 77, r])i(rj) drj''. 99) is valid for any r. 96), we obtain I 2C ju(OKOCdC= o 1. 100) that C = 1. This determines the function c(C) completely. 6). 102) give the complete solution to the problem of finding the radiation field in deep layers of the medium.