  The cross section for the elastic photoproduction of \r0 mesons ($\gamma p
\to \rho^0 p$) has been measured with the H1 detector at HERA for two average
photon-proton centre-of-mass energies of 55 and 187 GeV. TheFcenterline lower
energy point was measured by observing directly the $\rho^{0}$ decay giving a
cross section of $9.1\pm 0.9 (\stat)\pm 2.5 (\syst) \mu$b. The logarithmic
slope parameter of the differential cross section, ${\rm d}\sigma/{\rm d}t$, is
found to be $10.9 \pm 2.4 (\stat) \pm 1.1 (\syst) $GeV$^{-2}$. The \r0 decay
polar angular distribution is found to be consistent with s-channel helicity
conservation. The higher energy cross section was determined from analysis of
the lower part of the hadronic invariant mass spectrum of diffractive
photoproduction and found to be $13.6\pm 0.8 (\stat)\pm 2.4 (\syst) \mu$b.
