The surface of the nucleus is treated by a phenomenological and self-consistent statistical method, neglecting Coulomb effects, in an attempt to correlate such nuclear properties as the volume energy, surface energy, falloff distance, and mean radius. Assuming a value of \ensuremath{\sim}3.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm for the surface thickness we estimate the nuclear compressibility to be of the order of $125A+210{A}^{\frac{2}{3}}$ Mev. A thinner nuclear surface (the experimental value is 2.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm) would lead to larger values for the compressibility and conversely. The nuclear potential is found to extend \ensuremath{\sim}0.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm further in radius than the nuclear density.