With the assumption of nondivergent horizontal flow, harmonic wave solutions of the complete vorticity equation are obtained both for the plane and for the sphere. These solutions yield, for the velocity of propagation of the waves, formulae which are identical in form with those obtained by Haurwitz from an approximate linearized form of the vorticity equation. However, it is shown that these formulae must be interpreted quantitatively somewhat differently than heretofore. Qualitatively, the interpretation is unchanged. The motion of the waves toward the east decreases with increasing wave length, and increases with increasing westerly current.