  We test the validity of the black disk limit in elastic scattering by
studying the evolution of the dip in the scaling variable
$\tau=-t_{D}\sigma^{tot}$, where $t_{D}$ is the transverse momentum squared at
the dip and $\sigma_{tot}$ the total cross section. As $s\rightarrow \infty $
and $-t_{D} \rightarrow 0 $, $\tau$ may consistently be approaching the black
disc value, $\tau \xrightarrow[ \sqrt{s}\rightarrow \infty ]{} \tau_{BD}=35.92$
GeV$^{2}$ mb.
