  Cross sections for elastic and proton-dissociative photoproduction of J/psi
mesons are measured with the H1 detector in positron-proton collisions at HERA.
The data were collected at $ep$ centre-of-mass energies sqrt{s} approx 318 GeV
and sqrt{s} approx 225 GeV, corresponding to integrated luminosities of L = 130
pb^{-1} and L = 10.8 pb^{-1}, respectively. The cross sections are measured as
a function of the photon-proton centre-of-mass energy in the range 25< Wgp <
110 GeV. Differential cross sections $\mathrm{d}\sigma / \mathrm{d}t$, where
$t$ is the squared four-momentum transfer at the proton vertex, are measured in
the range $|t| < 1.2 \, \gevsq$ for the elastic process and $|t| < 8 \, \gevsq$
for proton dissociation. The results are compared to other measurements. The
$\Wgp$ and $t$-dependences are parametrised using phenomenological fits.
