The hypothesis is adopted that the Earth began as an entirely solid body and gradually became melted in its central regions. The incompressibilities of both the liquid and solid regions are linear functions of the pressure, and this enables an integral pressure-density relation to be found and also the effective uncompressed densities of the different regions. The equations for hydrostatic equilibrium can be reduced to a standard mathematical form, while Earth-models can be related to their solution by homologies with factors depending on the mass and physical constants of the material. An Earth of purely mantle-material and solid throughout would have radius 1.043 times the present radius, while allowance for lower uncompressed density of the outer layers increases this to 1.056R$_E$. This implies an initial surface area nearly 60 million square kilometres in excess of the present area. The liquid core-material is more compressible than the solid mantle-material at the pressures prevailing deep within the Earth, and it results that as the size of the core gradually increases, the composite Earth-model decreases in overall radius. The extreme lower limit of size corresponding to an entirely molten Earth would be 0.846R$_E$. The slow contraction of the entire Earth will gradually build up shearing stresses at and near the surface that the material there will eventually be unable to withstand, and periods of surface folding and thrusting will occur intermittently to relieve these stresses. Down to a depth of a few kilometres, less potential energy would be involved in piling up material against gravity than would be required in compressing it horizontally to maintain perfectly spherical form. The Earth would therefore prefer to buckle at the surface thereby remaining as uncompressed as possible at its outer parts. The theory suggests that Venus will have developed in much the same way as the Earth. On the other hand, because of the much lower pressures within the Moon, Mercury, and Mars, these objects are still solid throughout, and if melting ever occurs it would probably result in their expansion, not in contraction. Accordingly, thrusted and folded mountains would not be expected to be found on these bodies.