  The repeated passage of a coasting ion beam of a storage ring through a thin
target induces a shift in the revolution frequency due to the energy loss in
the target. Since the frequency shift is proportional to the beam-target
overlap, its measurement offers the possibility of determining the target
thickness and hence the corresponding luminosity in an experiment. This effect
has been investigated with an internal proton beam of energy 2.65 GeV at the
COSY-J\"ulich accelerator using the ANKE spectrometer and a hydrogen
cluster-jet target. Possible sources of error, especially those arising from
the influence of residual gas in the ring, were carefully studied, resulting in
a accuracy of better than 5%. The luminosity determined in this way was used,
in conjunction with measurements in the ANKE forward detector, to determine the
cross section for elastic proton-proton scattering. The result is compared to
published data as well as to the predictions of a phase shift solution. The
practicability and the limitations of the energy-loss method are discussed.
