The distributions of velocity potential over the water column for deriving both it the mild-slope equation and the Boussinesq equations have been unified. New equations of the Boussinesq type are derived by using the variational principle. The derived non-linear equations approach the Boussinesq equations in shallow water. The linear version is essentially the same as the mild-slope equation which is valid over the entire range of water depths. Numerical solutions of the new equations have been compared to experimental data and good agreement has been achieved.