A study has been made of the production of evaporation neutrons in the interactions of cosmic ray protons with lead nuclei. For the thick target used the mean number of neutrons produced (the mean `multiplicity') increases from 10 to 100 over the range of energy 0.2 to 200 GeV.At low energies, not greater than about 0.5 GeV, there is good agreement with the mean multiplicities computed by Metropolis et al. in 1958, but, as the energy increases, the observed multiplicities fall increasingly below expectation. At the highest energies, not less than about 10 GeV, there is evidence for a flattening of the multiplicity variation and the results are not inconsistent with a variation of the form expected from the Heisenberg model of the nucleon-nucleon collision.