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Recent ROSAT surveys suggest that galaxies constitute the new class of X-raysources required to explain the full phenomenology of the cosmic X-RayBackground (XRB). To test this hypothesis, we compute the two-pointcross-correlation function Wxg(theta) between 62 Einstein-IPC fields (.81-3.5keV) and the APM Northern galaxy catalog (13.5<E<19.0). At zero-lag (theta=0),we detect a 3.5sigma correlation signal with an amplitude ofWxg(0)=.045+/-.013. At non-zero lag (theta>0), the angular dependence of Wxghas two main features: the main signal for theta<4', and an almost flat plateauwith an amplitude of Wxg(theta>4')=.015, likely to result from the diffuseX-ray emission by clusters of galaxies. Taking the point-spread function of theX-ray instrument into account, we find that the mean X-ray flux of galaxieswith <E>=17.5+/-.3 is (8.1+/-4.7) 10^(-16) ergs/cm^2/s. This agrees with theX-ray flux expected from earlier direct studies of brighter galaxies, whichwere shown to result in a total galaxy contribution to the XRB of about 13%. Wediscuss how this powerful cross-correlation method can be used to measure theflux of X-ray sources well below the detection limit of X-ray instruments, and,perhaps, to probe otherwise undetectable faint diffuse X-ray emission.Comment: 52 LaTeX pages, 13 postscript figures, 3 tables, in AASTeX v4.0  format. To appear in ApJ, March 1, 1997, Vol. 47

Detailed Analysis of the Cross‐Correlation Function between the X‐Ray Background and Foreground Galaxies