The geopotential on and outside the earth is represented as a series in surface harmonics. The principal terms in it correspond to the solid harmonics of the external potential expansion with the coefficients being Stokes’ constantsCnm andSnm. The additional terms which occur near the earth’s surface due to its non-sphericity and topography are expressed in terms of Stokes’ constants too. This allows performing downward continuation of the potential derived from satellite observations. In the boundary condition which correlates Stokes’ constants and the surface gravity anomalies there occur additional terms due to the earth’s non-sphericity and topography. They are expressed in terms of Stokes’ constants as well. This improved boundary condition can be used for upward and downward continuations of the gravity field. Simple expressions are found representingCnm andSnm as explicit functions of the surface anomalies and its derivatives. The formula for the disturbing potential on the surface is derived in terms of the surface anomalies. All the formulas do not involve the earth’s surface in clinations.