The energy spectrum of cosmic rays above $2.5\times {10}^{18}\mathrm{eV}$, derived from 20 000 events recorded at the Pierre Auger Observatory, is described. The spectral index $\gamma$ of the particle flux, $J\propto E^{-\gamma }$, at energies between $4\times {10}^{18}\mathrm{eV}$ and $4\times {10}^{19}\mathrm{eV}$ is $2.69\pm 0.02(\mathrm{stat})\pm 0.06(\mathrm{syst})$, steepening to $4.2\pm 0.4(\mathrm{stat})\pm 0.06(\mathrm{syst})$ at higher energies. The hypothesis of a single power law is rejected with a significance greater than 6 standard deviations. The data are consistent with the prediction by Greisen and by Zatsepin and Kuz’min.

We describe the measurement of the depth of maximum, $X_{\max }$, of the longitudinal development of air showers induced by cosmic rays. Almost 4000 events above ${10}^{18}\mathrm{eV}$ observed by the fluorescence detector of the Pierre Auger Observatory in coincidence with at least one surface detector station are selected for the analysis. The average shower maximum was found to evolve with energy at a rate of $({106}_{-21}^{+35})\mathrm{g}/{\mathrm{cm}}^2/\mathrm{\text{decade}}$ below ${10}^{18.24\pm 0.05}\mathrm{eV}$, and $(24\pm 3)\mathrm{g}/{\mathrm{cm}}^2/\mathrm{\text{decade}}$ above this energy. The measured shower-to-shower fluctuations decrease from about 55 to $26\mathrm{g}/{\mathrm{cm}}^2$. The interpretation of these results in terms of the cosmic ray mass composition is briefly discussed.

We report a study of the distributions of the depth of maximum, $X_{\max }$, of extensive air-shower profiles with energies above $10^{17.8}\mathrm{eV}$ as observed with the fluorescence telescopes of the Pierre Auger Observatory. The analysis method for selecting a data sample with minimal sampling bias is described in detail as well as the experimental cross-checks and systematic uncertainties. Furthermore, we discuss the detector acceptance and the resolution of the $X_{\max }$ measurement and provide parametrizations thereof as a function of energy. The energy dependence of the mean and standard deviation of the $X_{\max }$ distributions are compared to air-shower simulations for different nuclear primaries and interpreted in terms of the mean and variance of the logarithmic mass distribution at the top of the atmosphere.