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We report the first ensemble results from the FUSE survey of molecularhydrogen in lines of sight with A_V $\gtrsim$ 1 mag. We have developedtechniques for fitting computed profiles to the low-J lines of H2, and thusdetermining column densities for J = 0 and J = 1, which contain $\gtrsim$99% ofthe total H2. From these column densities and ancillary data we have derivedthe total H2 column densities, hydrogen molecular fractions, and kinetictemperatures for 23 lines of sight. This is the first significant sample ofmolecular hydrogen column densities of 10^21 cm^-2, measured through UVabsorption bands. We have also compiled a set of extinction data for theselines of sight, which sample a wide range of environments. We have searched forcorrelations of our H2-related quantities with previously published columndensities of other molecules and extinction parameters. We find strongcorrelations between H2 and molecules such as CH, CN, and CO, in generalagreement with predictions of chemical models. We also find the expectedcorrelations between hydrogen molecular fraction and various density indicatorssuch as kinetic temperature, CN abundance, the steepness of the far-UVextinction rise, and the width of the 2175A bump. Despite the relatively largemolecular fractions, we do not see the values greater than 0.8 expected intranslucent clouds. With the exception of a few lines of sight, we see littleevidence for the presence of individual translucent clouds in our sample. Weconclude that most of the lines of sight are actually composed of two or morediffuse clouds similar to those found toward targets like zeta Oph. We suggesta modification in terminology to distinguish between a "translucent line ofsight" and a "translucent cloud."Comment: 64 pages in AASTeX preprint format, includes 12 figures and 11  tables; accepted for publication in Ap

AFar Ultraviolet Spectroscopic ExplorerSurvey of Interstellar Molecular Hydrogen in Translucent Clouds