On the relation between the proton-air cross section and fluctuations of the shower longitudinal profile

The current status and prospects of deducing the proton-air cross section from fluorescence telescope measurements of extensive air showers are discussed. As it is not possible to observe the point of first interaction, $X_ {\rm 1}$,directly,otherobservablescloselylinkedto$X_{\rm 1}$ must be inferred from the measured longitudinal profiles. This introduces a dependence on the models used to describe the shower development. Systematic uncertainties arising from this model dependence, from the reconstruction method itself and from a possible non-proton contamination of the selected shower sample are discussed.