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A region of almost 300~deg$^{2}$ in Ursa Major around the direction of the lowest neutral hydrogen column density in the sky has been surveyed in the $\frac{1}{4}$ keV X-ray band ($\sim0.12-0.284$~keV at 10\% of the peak response) using the ROSAT PSPC, and has been fully mapped in the 21~cm line of neutral hydrogen with an angular resolution of $21'$ or better. We present maps of these two data sets and an analysis of the spatial correlation between them. Over the entire field, the $\frac{1}{4}$~keV band X-ray count rate shows a strong negative correlation with the column density of Galactic neutral hydrogen. We discuss the local, extragalactic, and halo contributions to the observed diffuse X-ray intensity, and derive an upper limit to the Galactic X-ray emission originating beyond this HI distribution that is a factor of $\sim7$ smaller than the inferred flux from beyond the Draco Nebula, an apparent halo object located $\sim41\deg$ away. This implies that while there may be significant amounts of hot gas in the galactic halo, its properties must vary strongly across the sky.
This research was supported in part by the National Aeronautics and Space Administration under grants NAG5-679, NAG5-1726, and NAG5-1817 and by the Max Planck Institute for Extraterrestrial Physics.
