A search has been conducted for massive, long-lived, weakly interacting particles (i.e., leptons) in cosmic radiation at a depth of 7.6 hg/sq cm. The search was made with a velocity-discriminated charged-particle range spectrometer where subrelativistic particles are detected by a system of scintillation and Cerenkov counters. The technique consisted of selecting charged particles with a scintillator-counter telescope and vetoing relativistic particles with a water Cerenkov detector. Particle range was observed in arrays of neon flash tubes interspersed with iron absorbers. Observations made for a 3000-hour period showed 28 events which satisfied the trigger and event selection criterion. Most events were considered to be caused by low-energy recoil protons from high-energy muon inelastic scattering. The observed events are consistent with the background. Heavy leptons were not recorded. A ratio having a limit of 2.12 x 10 to the -7th power was established for the flux of heavy leptons to that of all muons at the depth considered.