Summary The hypothesis has been set down that at pressures ranging from 0.4 × 1012 to at least 3.6 × 1012 dynes/cm.2 (the latter being the pressure at the Earth's centre) the compressibility K−1 of a substance at temperatures of the order of those in the Earth's deep interior is essentially independent of its chemical composition. A simple form of the hypothesis to the effect that K and dk/dp (where p denotes pressure) change continuously and smoothly throughout the Earth below a depth of 1000 km. has been discussed in relation to seismic data. The hypothesis entails an abnormally large density gradient in the lowest 200 km. of the Earth's mantle, and in the Earth's inner core, and that these two regions are not chemically homogeneous. It entails that the density near the Earth's centre lies between about 16 g./cm.3 and 20 g./cm.3 (apart from a possible accumulation of even denser material very close to the centre). The hypothesis in its simplest form would require the Earth's density to be a little higher in the region above the 1000-km. level than the figures given in a previous model. The hypothesis would entail that the inner core is solid, capable of transmitting S waves at a speed not less than about 4.9 km./sec. and probably less than 6.0 km./sec.