(Summary) The functional conditions referring the anomalous potential have been worked out by the integral formula of Green. The value of the functionals over the continental areas has been calculated by the measured values of the gravity anomaly and the components of deflection of the vertical or of the geopotential number and for ocean areas by the measured values of the gravity disturbance or of the boundary values of the potential. The functional problem has been reduced to the restoration of the
finite-dimensional and unique geopotential which satisties the functional cxonditions best /in least-squares sense/. The discretisation of the functional could be carried out by means of a complete system of expansion unorthogonal functions. By the preliminary orthonormalization of this system the problem has been reduced to a system of linear equations, referring the coeficients of Fourier in the expansion of the potential. We propose four spherical solutions of the altimetry-gravimetry boundary problem by a discrete description and two in a closed form by a generalisation of the function of Stokes and Neumann /Hotine kernel/.