Shower Center of Gravity and Hadronic Interaction Characteristics
  Equations for the center of gravity of the shower originated by high energy proton in the atmosphere are written and, within certain simplifications, solved for the case of logarithmically decreasing interaction length of hadrons in the air. Obtained expression provides transparent view of the way in which hadronic interaction characteristics determine the longitudinal shower development. 
Lev Kheyn
astro-ph.HE