The densities of methane, metallic ammonium, water and neon are caluclated at pressures up to 20 million atmospheres. The computed densities of methane and neon are based mainly on molecular scattering at high energies, which yield the inter-molecular forces at close approach. The calculations of Bernal and Massey on metallic ammonium are extrapolated to higher pressures. The computed densities of water are based on high-pressure shock wave experiments recently carried out in the United States and Russia. The pressure-density relationship of CHONNE material (which is a mixture of methane, metallic ammonium, water and neon in cosmic proportions) is also computed. It is shown that Uranus and Neptune have lost or failed to capture most, but not all, of the free hydrogen in cosmic material. The figures of these planets indicate that they contain central cores of heavy (presumably terrestrial) materials. The large difference in the mean densities of Uranus and Neptune suggests that water becomes metallic at a pressure intermediate between the central pressures of these planets.