A method is given which permits the calculation of the volumes of aqueous solutions of salts at higher pressures solely from the volumes of these solutions at atmospheric pressure and the compressibility data of the pure substances involved. The volumes of aqueous solutions of sodium chloride, ammonium nitrate, and potassium sulfate are computed to 10 000 bars pressure and these agree with the observed values to within a fraction of one percent. Tammann's hypothesis, to the effect that water in solution is compressed by an ionized solute, is used; but, the extension of this hypothesis permits the calculation of the volumes of the solute and the water in solution and the effect of pressure on these volumes. The interpolation formulas derived also appear to be applicable to nonaqueous solutions of salts; and some tentative results are also given for mixtures of liquids (ethyl alcohol in water). An equation is introduced, which like Tait's equation, represents the variation of volumes with pressure. This equation is fundamental to the development of the interpolation equations for solutions which are given in this article. It is found that an analogous equation reproduces refractive index and dielectric constant data for liquids and gases at high pressures. This leads to an equation, previously proposed, which is considered more useful in representing experimental data analytically than the corresponding formulas of Lorenz-Lorentz and Mossotti-Clausius.