Measurements of the cosmic ray composition with air shower experiments

In this paper we review air shower data related to the mass composition of cosmic rays above 10¹⁵ eV. After explaining the basic relations between air shower observables and the primary mass and energy of cosmic rays, we present different approaches and results of composition studies with surface detectors. Furthermore, we discuss measurements of the longitudinal development of air showers from non-imaging Cherenkov detectors and fluorescence telescopes. The interpretation of these experimental results in terms of primary mass is highly susceptible to the theoretical uncertainties of hadronic interactions in air showers. We nevertheless attempt to calculate the logarithmic mass from the data using different hadronic interaction models and to study its energy dependence from 10¹⁵ eV to 10²⁰ eV.