Solberg's theory of oscillations and waves of short wave length unaffected by the earth's rotation in an atmosphere with a linear temperature field is extended for a vertical wind shear. Under normal conditions in the atmosphere this extension means only a small and insignificant correction of Solberg's theory provided the wind velocity is different from the wave velocity. If the wave velocity is equal to the wind velocity in a particular level then the theory presented in this paper requires an adiabatic or superadiabatic temperature gradient in the layer containing this particular level. This theory, applied to the theory of billow clouds generalized for the case when the sharp discontinuity is replaced by a transition layer with continuous distribution of wind velocity, provides not only the necessary conditions for the existence of billow clouds, requiring a neutral (adiabatic) or unstable stratification in the transition layer, but also determines the form of the cellular pattern of such waves in terms of their dependence on the wind shear. Transversal waves-normal to the general motion-and rectangular patterns can exist only with a small wind shear; for larger values of shear they change into longitudinal waves (strips) parallel to the general motion. The observations of billow clouds made by Ma1 and the experiments with artificial clouds-unstable layers heated from below in a motion with strong shear-made by Idrac, Walker, Phillips, and others, confirm the existence of the adiabatic or superadiabatic gradient in the transition layer and the change of form of the cells with increasing wind shear, required by the theory.