A direct determination has been made of the cosmic ray spectrum underground at a depth of 38 m.w.e. under Castle Rock, Nottingham. The spectrum is based on measurements of 1010 particles traversing a magnetic spectrograph having a maximum detectable momentum of 8 GeV/c. By comparing this spectrum with the ground-level spectrum the energy loss of fast $\mu $-mesons in penetrating the 38 m.w.e. of rock has been determined. It is shown that the energy loss for $\mu $-mesons in the momentum range 7 to 15 GeV/c is as expected by theory, the collision process being responsible for most of the loss.