  The shape of the longitudinal development of the showers generated in the
atmosphere by very high energy cosmic ray particles encodes information about
the mass composition of the flux, and about the properties of hadronic
interactions that control the shower development. Studies of the energy
dependence of the average and width of the depth of maximum distribution of
showers with $E \gtrsim 10^{17.3}$ eV measured by the Pierre Auger Observatory,
suggest, on the basis of a comparison with current models, that the composition
of the cosmic ray flux undergoes a very important evolution, first becoming
lighter and then rapidly heavier. These conclusions, if confirmed, would have
profound and very surprising implications for our understanding of the high
energy astrophysical sources. Studies of the shape of the depth of maximum
distribution in the same energy range have been used by Auger and by the
Telescope Array Collaboration to measure the interaction length of protons in
air, a quantity that allows to estimate the $pp$ cross sections for values of
$\sqrt{s}$ well above the LHC range. In this paper we argue that it is
desirable to combine the studies of the cosmic ray composition with those aimed
at the measurement of the $p$--air cross section. The latter allow to obtain
estimates for the fraction of protons in the flux that can be of great help in
decoding the composition and its energy dependence. Studies that consider
multiple parameters to characterize the depth of maximum distributions also
offer the possibility to perform more sensitive tests of the validity of the
models used to describe high energy showers.
