  We use 2n streams, where n is an integer, of axially symmetric radiation to
solve the equation of transfer for a layered medium. This is a generalization
of Schuster's classic 2 stream model. As is well known, using only the first 2n
Legendre polynomials to describe the angular dependence of radiation reduces
the equation of transfer to a first order differential equation in a space of
2n dimensions. It is convenient to characterize the radiation as 2n stream
intensities propagating at zenith angles having cosines called the 2n
Gauss-Legendre cosines defined to be solutions of equating the Legendre
polynomial of degree 2n to zero. We show how to efficiently and accurately
solve the equation of transfer with vector and matrix methods analogous to
those used to solve Schroedinger's equation of quantum mechanics. To model
strong forward scattering, like that of visible light by Earth's clouds, we
have introduced a new family of phase functions. These give the maximum
possible forward scattering p(p+1) for a phase function constructed from the
first 2p Legendre polynomials, where p is an integer. We show illustrative
examples of radiative-transfer phenomena calculated with this new method.
