  The Heitler-Matthews model for hadronic air showers will be extended to all
the generations of electromagnetic subshowers in the hadronic cascade. The
analysis is outlined in detail for showers initiated by primary protons. For
showers initiated by iron primaries the part of the analysis is given for as
far as it differs from the analysis for a primary proton. Predictions for
shower sizes and the depth of maximum shower size are compared with results of
Monte Carlo simulations. The depth of maximum as it follows from the
extrapolation of the Heitler-Matthews model restricted to the first generation
of electromagnetic subshowers is too small with respect to Monte Carlo
predictions. It is shown that the inclusion of all the generations of
electromagnetic subshowers leads to smaller predictions for the depth of
maximum and to smaller predictions for the elongation rate. The discrepancy
between discrete model predictions and Monte Carlo predictions for the depth of
maximum can therefore not be explained from the number of generations that is
taken into consideration. An alternative explanation will be proposed.
