A search for evidence of Hard Single Diffraction (HSD) in forward and central jet systems is described for center-of-mass energies of 1800 and 630 GeV. Events are examined for the presence of a forward rapidity gap with concurrent jet production. Relative event rates are estimated for both processes as compared to an inclusive dijet data sample, and the distributions of Pomeron x in the proton, called xi, are also measured for both forward and central HSD events, The data measurements are compared to the Ingelman-Schlein model.