Motivated by some results from barotropic models, a linearized steady-state five-layer baroclinic model is used to study the response of a spherical atmosphere to thermal and orographic forcing. At low levels the significant perturbations are confined to the neighborhood of the source and for midlatitude thermal forcing these perturbations are crucially dependent on the vertical distribution of the source. In the upper troposphere the sources generate wavetrains which are very similar to those given by barotropic models. For a low-latitude source, long wavelengths propagate strongly polewards as well as eastwards. Shorter wavelengths are trapped equatorward of the poleward flank of the jet, resulting in a split of the wave-trains at this latitude. Using reasonable dissipation magnitudes, the easiest way to produce an appreciable response in middle and high latitudes is by subtropical forcing. These results suggest an explanation for the shapes of patterns described in observational studies.The theory for waves propagating in a slowly varying medium is applied to Rossby waves propagating in a barotropic atmosphere. The slow variation of the medium is associated with the sphericity of the domain and the latitudinal structure of the zonal wind. Rays along which wave activity propagates, the speeds of propagation, and the amplitudes and phases along these rays are determined for a constant angular velocity basic flow as well as a more realistic jet flow. They agree well with the observational and numerical model results and give a simple interpretation of them.