The UA8 experiment previously reported the observation of jets in diffractive events containing leading protons ("hard diffraction"), which was interpreted as evidence for the partonic structure of an exchanged Reggeon. believed to be the Pomeron. In the present Letter, we report the final UA8 hard-diffractive (jet) cross section results and their interpretation. After corrections, the fraction of single diffractive events with mass from 118 to 189 GeV that have two scattered partons, each with E-T(jet) > 8 GeV, is in the range 0.002 to 0.003 (depending on x(p)). We determine the product, fK, of the fraction by which the Pomeron's momentum sum rule is violated and the normalization constant of the Pomeron-Flux-Factor of the proton. For a pure gluonic- or a pure q (q) over bar-Pomeron, respectively: fK = (0.30 +/- 0.05 +/- 0.09) and (0.56 +/- 0.09 +/- 0.17) GeV-2. (C) 1998 Published by Elsevier Science B.V.