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An extension of Bjerhammar’s translocation to the involvement of the 1st order of contribu-tion of the flattening of an ellipsoid has been developed to be in keeping with a special pur-pose of higher accuracies. To complete it, we follow this way: (i) to carry out a new Poisson in-tegral involving the effect of the flattening, (ii) to solve the so-called simple Robin problemfor an ellipsoid on a boundary condition of radial derivative, and (iii) to derive a solution ofgeneral Robin problem in the case of an ellipsoid via the solution of simple Robin problem aftertransforming boundary conditions from normal derivative into radial derivative. Finally, the useof the combination of the solution of general Robin problem with the generalized Poisson inte-gral with respect to the regular harmonic function r△g on the linearized Molodensky problemfor an ellipsoid makes a definition of the desired translocation in the case of an ellipsoid. Ob-viously, this developed translocation will go back to the traditional
An extension of Bjerhammar’s translocation to the involvement of the 1st order of contribu-tion of the flattening of an ellipsoid has been developed to be in keeping with a special pur-pose of higher accuracies. To complete it, we follow this way: (i ) to carry out a new Poisson in-tegral involving the effect of the flattening, (ii) to solve the so-called simple Robin problem for an ellipsoid on a boundary condition of radial derivative, and (iii) to derive a solution ofgeneral Robin problem in the case of an ellipsoid via the solution of simple Robin problem aftertransforming boundary conditions from normal derivative into radial derivative. Finally, the use of the combination of the solution of general Robin problem with the generalized Poisson inte-gral with respect to the regular harmonic function r △ g on the linearized Molodensky problem for an ellipsoid makes a definition of the desired translocation in the case of an ellipsoid. Ob-viously, this developed translocation will go back to the traditional