  In this paper we prove a new optimal bound on the logarithmic slope of the
elastic slope when: elastic cross section and differential cross sections in
forward and backward directions are known from experimental data. The results
on the experimental tests of this new optimal bound are presented in Sect. 3
for the principal meson-nucleon elastic scatterings: pion-nucleon, kaon-nucleon
at all available energies. Then we have shown that the saturation of this
optimal bound is observed with high accuracy practically at all available
energies in meson-nucleon scattering.
