  The diffractive photoproduction of J/psi mesons is measured with the H1
detector at the ep collider HERA using an integrated luminosity of 78 pb^-1.
The differential cross section d sigma(gamma p -> J/psi Y) / d t is studied in
the range 2 < |t| < 30 GeV^2, where t is the square of the four-momentum
transferred at the proton vertex. The cross section is also presented as a
function of the photon-proton centre-of-mass energy W in three t intervals,
spanning the range 50 < W < 200 GeV. A fast rise of the cross section with W is
observed for each t range and the slope for the effective linear Pomeron
trajectory is measured to be alpha^\prime= -0.0135 \pm 0.0074 (stat.) \pm
0.0051 (syst.) GeV^-2. The measurements are compared with perturbative QCD
models based on BFKL and DGLAP evolution. The data are found to be compatible
with s-channel helicity conservation.
