  We derive the usual Oberbeck--Boussinesq approximation as a constitutive
limit of the full system describing the motion of an compressible linearly
viscous fluid. To this end the starting system is written, using the Gibbs free
energy, in the variables $\mathbf v, \theta$ and $p$. The Oberbeck--Boussinesq
system is then obtained as the thermal expansion coefficient $\alpha$ and the
isothermal compressibility coefficient $\beta$ tend to zero.
