  We present measurements of interstellar H_2 absorption lines in the continuum
spectra of seven early-type stars in the Galactic disk at distances between 1
and 4 kpc. Five of these stars provide lines of sight through the Sagittarius
spiral arm. The spectra, obtained with the Berkeley EUV/FUV spectrometer on the
ORFEUS telescope in 1993 September, have a resolution of 3000 and statistical
signal-to-noise ratios between 20 and 80. We determine column densities for
each observed rotational level and derive excitation temperatures and densities
for the H_2 clouds along each line of sight. Our data continue the
relationships among H_2 column density, fractional molecular abundance, and
reddening apparent in Copernicus observations of nearby stars, indicating a
common mechanism for H_2 production. Estimates of cloud temperatures and
densities are consistent with those derived from Copernicus data. We find that
the molecular fraction of hydrogen is nearly constant over a wide range of
distances and mean reddenings, consistent with a model in which a significant
fraction of the neutral ISM is associated with H_2-bearing molecular clouds,
even along low-density lines of sight.
