  Cross sections for proton inelastic collision with different nuclei are
described within the Glauber and multiple scattering approximations. A
significant difference between approximate `Glauber' formula and exact
calculations with a geometrical scaling assumption for very high-energy cross
section is shown. Experimental values of proton-proton cross sections obtained
using extensive air shower data are based on the relationship of proton-proton
and respective proton-air absorption cross sections. According to obtained
results values reported by the Akeno and Fly's Eye experimental groups are
about 10% overestimated. The proper energy dependence of absorption cross
section for collisions with air nuclei is of a great importance for studies of
high energy cosmic rays using the Monte Carlo technique.

High Energy Physics - Phenomenology