The configuration of a free liquid film, free liquid filament, and the Plateau border in a gravitational field is studied based on the general condition of the mechanical equilibrium for capillary objects. The Archimedian convection in the films is described. The linear tension of the unduloid and the Plateau border is calculated at zero and finite contact angles between the meniscus and the film. Gravitational field-induced deviations from the Plateau rule for the angles betwen three films crossing at the horizontal Plateau border are estimated.