| Summary: | Calculations have been made to investigate the effects on high energy muon showers of varying some of the more important parameter of high energy nucleon-air nucleus collisions. The effects of different assumptions concerning the primary mass composition have also been investigated. The majority of the calculations have been deigned to enable a comparison to be made with the experimental results of the Utah group on underground muons with threshold energies of the order of 1000 GeV, and above, and zenith angles in the region of 60º. Assuming the primary composition to be similar to that found at primary energies ~ 10 GeV, it is concluded that if the multiplicity of secondary particles varies as E(_p)(^¼) then the value of the mean transverse momentum is 0.67 ± 0.1 GeV/c at primary energies ~2 10 (^5)GeV, and if the multiplicity varies as E(_p)(^½) a value of ~0.5 GeV/c is obtained at energies ~ 4 10(^5)GeV. Using a value of 0.4 GeV/c for the mean transverse momentum, all the models predict significantly more muons than observed. An increase in the mean transverse momentum and/or the energy loss coefficient, b, are considered the most likely parameter changes to give better agreement. The present work favours a multiplicity law varying as E(_p)(^¼) rather than one varying as E(_p)(^½) but this cannot be regarded as conclusive. As yet, due to lack of experimental data, no conclusion have been made possible concerning the primary mass composition but there is no evidence for an increase in the proportion of heavy nuclei above 10(^12)eV as concluded by Grigorov et al. (1967). The present work does not rule out the possibility of some muons in E.A.S. being produced by a process other than the decay of pions and kaions.
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