Radiative transfer through a model plane-parallel grey atmosphere is invest
igated. For the purposes of this study the atmosphere is considered to cons
ist of a stationary, inviscid and incompressible fluid. A definitive descri
ption of this state is essential for an analysis of the convective instabil
ity of such an atmosphere, which will be considered in later papers. The fl
uid is assumed to be in local thermodynamic equilibrium (LTE) and the treat
ment of the radiation field is simplified through the use of the Eddington
approximation. This results in a pair of simultaneous equations for the tem
perature and mean radiative intensity. It is shown that the structure of th
e atmosphere, under the assumption of convective stability, depends on two
dimensionless parameters which can be related to the ratio of radiative to
conductive heat transfer and the ratio of layer depth to photon mean free p
ath. Analysis reveals that when the bulk of the atmosphere is in radiative
equilibrium boundary layers are required at the upper and lower surfaces in
order to satisfy the appropriate boundary conditions. The structure of the
se boundary layers is analyzed through the method of asymptotic matching. T
hese results predict structure of the temperature and mean intensity at the
parameter extremes appropriate for both planetary and stellar applications
.