A new statistical procedure is described for obtaining the thermodynamic properties of a molecular system directly as functions of the pressure. This procedure differs in principle from that suggested by Guggenheim [3] in that the members of the representative ensemble are envisaged as being in constant mechanical equilibrium with the exterior. The quantal and classical theories of petit micro-canonical and canonical ensembles of systems at constant pressure are presented, and shown to lead to the established results for perfect and imperfect gases, and for a hypothetical one-dimensional system. The conclusion that the statistical compressibility of a molecular system is essentially positive follows directly from the theory. An alternative procedure which leads to a more satisfactory form of Guggenheim's equation is also described, and its relation to the new approach is shown.