In ship manoeuvring studies, the derivatives in the equations of motion must be known for the particular ship. Determined by calculation or experiment in deep water, problems arise in shallow water, since the derivatives depend on water depth, as well as on ship geometry. Errors have been found in a semi-empirical correction method published previously. Potential flow calculations involving conformal mapping allow revised equations to be deduced for hulls with elliptical body sections, and a new relationship is suggested for hulls with rectangular body sections. These equations can then be used to correct the deep-water derivatives to any shallow-water condition.