When salt water displaces fresh water in sand the boundary between the two liquid phases becomes diffuse after a short period of flow. The dispersion of salt may occur at a much greater rate than can be expected by ion diffusion. The effect has been attributed to a mechanism referred to here as hydrodynamic dispersion, a general phenomenon arising from the fact that the velocity of the moving stream varies from point to point in the porous system.The mathematical treatment of the problem is based upon a statistical theory developed by Scheidegger. Equations have been derived here for the dispersion of salt water injected in the stream. The theory has been tested by displacing pure water with salt water in a column of saturated sand and determining the concentration of effluent as a function of time. The measured concentrations vary with time in approximately the manner predicted by theory.