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The diffusion equations describing the unidimensional propagation of .the high energy nucleonic component of cosmic rays throughout the atmosphere are sol"V'ed under two assumptions: (l) The nucleon-nucleon collisions are described according to Fermi's therlnOdynamical model involving completely inelastic pion and.nucleon-antinucleon pair production. (2) A somewhat opposite assumption is made assuming partially elastic collisions without nucleon-anti.nucleon pair production. Due to the present inaccuracy of experiments, we are able to derive only tentati v.e conclusions. The values computed under both hypotheses for the absorption mean free path and the charged to neutral particles ratio are found in acceptable ranges when compared to experimental data. The differential energy spectrum at a given depth is always found steeper than the primary, and steeper than indicated by experimental values if the primary is taken proportional to the 2.5 inverse power of energy.