We report measurements of the inclusive differential cross section for the single-diffractive reactions p(i) + (p) over bar --> p(f) + X and p + <(p)over bar (i)> --> X + <(p)over bar (f)> at root s = 630 GeV, in the momentum transfer range 0.8 < -t < 2.0 GeV2 and final-state Feynman-x(p) > 0.90. Based on the assumption of factorization, several new features of the pomeron flux factor are determined from simultaneous fits to our UA8 data and lower energy data from the CHLM collaboration at the CERN Intersecting Storage Rings. Prominent among these is that the effective pomeron Regge trajectory requires a term quadratic in t, with coefficient alpha " = 0.079 +/- 0.012 GeV-4. We also show that the data require a pomeron-proton cross section that first decreases with increasing diffractive mass (corresponding to the PPR term in the triple-Regge expansion) and then increases at larger mass (the PPP term), similar to real particle total cross sections. We measure the product K sigma(0) = 0.72+/-0.10 mb GeV-2 where K is the normalization constant of the pomeron flux factor in the proton and ao is the scale constant in the pomeron-proton total cross section. Finally, we report the occurrence of "beam jets" in the pomeron direction in the rest frame of the diffractive system. (C) 1998 Elsevier Science B.V.