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We report the first direct measurement of the thermal pressure of the hot phase of the interstellar medium (ISM). This result is derived from the discovery of a shadow in the diffuse extreme ultraviolet background with the Extreme Ultraviolet Explorer (EUVE) Deep Survey telescope Lexan/boron filter (65--190~\AA). Variations in the diffuse EUV intensity observed along a 24-day scan of the ecliptic plane were found to be spatially anti-correlated with the IRAS 100 $\mu$m intensity of these regions. An individual absorption feature at $l \sim 165$, $b \sim -32$ was found to coincide with an isolated IRAS cirrus cloud, which though tenuous by usual standards, is optically thick at EUV wavelengths. The EUV intensity at the absorption feature yields the emission measure of the hot ISM in the line of sight to the cloud. The distance to the cloud has been found from optical work. These two results are combined to yield a direct determination of the thermal pressure. The value obtained is ${\rm p/k} \simeq 19,000$, which is almost a factor of seven larger than the most commonly assumed value. This work has been supported by NASA contract NAS5-30180.
