Calculations are made of the free energies of hydration of simple ions on the basis of a continuous dielectric model in which allowance is made for the variation of dielectric constant with field strength. The ion is considered to be a point charge contained in a volume having the same dielectric properties as the dielectric continuum. The effective radii in solution are taken to be the crystal radii increased by 25 %. Halliwell and Nyburg's value of the absolute hydration enthalpy of the proton is used to obtain a set of individual ionic free energies of hydration. Their method is also used to correct the calculated free energies for the specific orientation of water molecules. The agreement between calculated and observed values is satisfactory.