L. N. Howard proved an inequality concerning the complex velocity of the propagation of waves disturbing the laminar, unidirectional flow of an incompressible stratified fluid. It is shown that this theorem is closely related to the virial theorem of hydrodynamics. It can be generalized for the steady motion of a compressible fluid, provided the streamlines are either parallel straight lines or coaxial circles. The connection of the circle and virial theorems provides an interpretation of the former in terms of the energy of the perturbation. A positive potential energy always exerts a stabilizing influence, as does the angular velocity in the case of circular streamlines. This latter is diminished for short waves; it is also complicated by the fact that radial variations of the angular velocity may contribute negative terms to the potential energy. Zonal flow, such as the jet stream of the Earth's atmosphere, is generally baroclinic. In the barotropic case, the potential energy of the perturbation is simply proportional to the Va¨isa¨la¨‐Brunt frequency. In the baroclinic case, this frequency cannot be usefully defined, and the more elaborate formulae are derived.