Abstract
Due to the high energy interactions of cosmic ray particles, progressive showers of secondary particles initiate in the atmosphere. Several models are suggested to describe the longitudinal development of extensive air showers, for example the Heitler model. The Heitler model also is written for hadronic showers. Anyhow, the predicted values of $X_{max}$ may differ significantly with the values from detailed simulations by up to about $100~(\mbox{g}/\mbox{cm}^{2})$ . In the present work, the mean depth of shower maximum is calculated using a variable interaction length. New equations for $X_{max} $ in the electromagnetic and hadronic showers have been obtained.
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