In Naeser (1979), later denotedN, it was shown that a frequency shift of a wave spectrum had to be expected as a result of dissipation of energy and conservation of spin of the waves. While time-dependency was treated inN, mainly space-dependency is treated here. In order to do this, the velocity of the spin of the waves is calculated. It is shown that this can be made equal to the group velocity by a second order coordinate transformation. In the limits of deep and shallow water the transformation becomes the identity, and leaves the Stokes drift at its usual value if the moment point is located at the mean water level.