The time structure of the signals from air showers, recorded with the water-Cherenkov detectors of the Pierre Auger Observatory, contains information that can be related to the mass composition of primary cosmic rays and to hadronic multi-particle production. We can study both because the recorded signals contain a mix of the muonic and electromagnetic components. Using information from the time structure, we define observables that enable a comparison of observations with predictions from hadronic models. We have found that the interpretation obtained from a comparison of our data to these predictions is inconsistent with the interpretation obtained by comparing fluorescence measurements and model predictions, over a greater energy range, and with higher precision, than in previous studies. Information about mass composition is obtained by calibrating the observables based on time structure with fluorescence measurements. Following this approach, we infer the depth of shower maximum, Xmax, from 0.3 EeV to over 100 EeV. In particular, above 30 EeV, our sample is nearly fourteen times larger than currently available from fluorescence measurements. With this novel approach we find good agreement with previous studies and, with our larger sample, we have extended the measurement of <Xmax> to greater energies than
hitherto.