  A study is presented of the process gamma p -->XY, where there is a large
rapidity gap between the systems X and Y. Measurements are made of the
differential cross section as a function of the invariant mass mx of the system
produced at the photon vertex. Results are presented at centre of mass energies
of W_gp = 187 GeV and W_gp = 231 GeV, both where the proton dominantly remains
intact and, for the first time, where it dissociates. Both the centre of mass
energy and the mx^2 dependence of HERA data and those from a fixed target
experiment may simultaneously be described in a triple-Regge model. The low
mass photon dissociation process is found to be dominated by diffraction,
though a sizable subleading contribution is present at larger masses. The
pomeron intercept is extracted and found to be alpha_pom(0) = 1.068 \pm 0.016
(stat.) \pm 0.022 (syst.) \pm 0.041 (model), in good agreement with values
obtained from total and elastic hadronic and photoproduction cross sections.
The diffractive contribution to the process gamma p --> Xp with mx^2 / W_gp^2 <
0.05 is measured to be 22.2 \pm 0.6 (stat.) \pm 2.6 (syst.) \pm 1.7 (model) %
of the total gamma p cross section at W_gp = 187 GeV.
