General Solution of the Problem of Hydrostatic Equilibrium of the Earth

Summary If de Sitter's hydrostatic equations are developed independent of the external potential theory, the hydrostatic geopotential coefficient J h occurs explicitly on the right‐hand side of these equations. Since this J h has to be treated as an unknown in the solution of the problem, it becomes rather difficult to solve these hydrostatic equations independently, regardless of which of the dynamical parameters associated with the Earth is taken as the initial datum. The solution of these equations is possible, however, with the help of a boundary condition derived from the external potential theory which neither assumes nor discounts the presence of equilibrium conditions in the Earth's interior. If a general solution is constructed on these lines, the three particular solutions, usually quoted in literature, stem from it in the wake of the appropriate assumptions. Of course, out of these the only meaningful solution is that corresponding to the polar moment of inertia as the initial datum. It is essential that the solution be constructed in this way in order to demonstrate clearly the correct structure of the problem of hydrostatic equilibrium. The anomalous gravity field of the Earth referred to the hydrostatic figure is compared with that referred to the international reference ellipsoid.