The analysis of an earlier paper (Busse l970a) in which the differential rotation of the Sun was explained as the result of large scale convection in the solar convection zone is extended to include the detailed spatial dependence of the meridional circulation as well as of the differential rotation. The thin shell approximation for a rotating spherical convection layer of a Boussinesq fluid is used. The asymptotic representation of large order spherical harmonlcs by Hermite functions permits a simple integration of the equations for the meridional circulation and the differential rotation. Explicit analytical solutions are given for the case of stressfree boundaries and numerical results are shown in the case of a rigid inner and a free outer boundary. The case of stressfree boundaries is rather exceptional and the magnitude of the differential rotation is reduced for more general boundary conditions. However, the differential rotation still exhibits the characteristic equatorial acceleration in the case of an inner rigid boundary. (auth)