An apparatus consisting of a stack of six scintillation counters interleaved with lead target material has been operated in underground laboratories at depths below the top of the atmosphere of 72 and 460 hg cm-". The probability that a muon transferred secondary energy in the range 0.1 to 30 GeV was determined from the recorded data. At the shallower depth the dominant process was knock-on and at the greater depth direct pair production was more significant. By comparing the rates of electromagnetic interactions at the two depths it was possible to make an estimate of the contribution due to pair production which was relatively insensitive to systematic errors. For secondary energies in the range 0.1 to 5 GeV the results confirm the theoretical predictions for both knock-on and pair production to within about 15% in each case.