  We study the influence of shower fluctuations, and the possible presence of
different nuclear species in the primary cosmic ray spectrum, on the
experimental determination of both shower energy and the proton air inelastic
cross section from studies of the longitudinal development of atmospheric
showers in fluorescence experiments. We investigate the potential of track
length integral and shower size at maximum as estimators of shower energy. We
find that at very high energy (~10^19-10^20 eV) the error of the total energy
assignment is dominated by the dependence on the hadronic interaction model,
and is of the order of 5%. At lower energy (~10^17-10^18 eV), the uncertainty
of the energy determination due to the limited knowledge of the primary cosmic
ray composition is more important. The distribution of depth of shower maximum
is discussed as a measure of the proton-air cross section. Uncertainties in a
possible experimental measurement of this cross section introduced by intrinsic
shower fluctuations, the model of hadronic interactions, and the unknown
mixture of primary nuclei in the cosmic radiation are numerically evaluated.
