  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 $\sigma_{\rm elas}/\sigma_{\rm tot}
\rightarrow 1/2$, and that $8\pi B/\sigma_{\rm tot}\rightarrow 1$ at very high
energies, where $B$ the forward slope parameter for the differential elastic
scattering cross sections. The relations demonstrate convincingly that the
asymptotic $pp$ and $\bar{p}p$ 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.
