We demonstrate that the entirety of the data on proton-proton and antiproton-proton forward scattering between 6 GeV and 57 TeV center-of-mass energy is sufficient to show that σ elas /σtot → 1/2, and that 8πB/σtot → 1 at very high energies, where B the forward slope parameter for the differential elastic scattering cross sections. The relations demonstrate convincingly that the asymptotic pp andpp scattering amplitudes approach those of scattering from a black disk. This result obviously has implications for any new physics that modifies the forward scattering amplitudes.