V. The construction and analysis of geometrical propositions, determining the positions assumed by homogeneal bodies which float freely, and at rest, on a fluid's surface; also determining the stability of ships, and of other floating bodies

Abstract

To investigate the positions assumed by homogeneal bodies which float freely, and at rest, on a fluid's surface, it is necessary, in the first place, to form a just conception of the several principles on which those positions depend. The proportion of the immersed part to the whole magnitude of a floating body will always be obtained, from having given the specific gravity of the solid in respect to that of the fluid; since it is a known law of hydrostatics, that the immersed part of the solid is to the whole magnitude, in the proportion of those specific gravities. But a solid may be immersed in a fluid numberless different ways, so that the part immersed shall be to the whole magnitude in the given proportion of the specific gravities, and yet the solid shall not rest permanently in any of these positions.