Bounds on the phase velocity in the linear instability of viscous shear   flow problem in the $\beta$-plane
  Results obtained by Joseph ({\it J. Fluid Mech.} {\bf 33} (1968) 617) for the viscous parallel shear flow problem are extended to the problem of viscous parallel, shear flow problem in the beta plane and a sufficient condition for stability has also been derived. 
R G Shandil and Jagjit Singh