We present measurements of interstellar H-2 absorption lines in the co
ntinuum spectra of seven early-type stars in the Galactic disk at dist
ances between 1 and 4 kpc. Five of these stars provide lines of sight
through the Sagittarius spiral arm. The spectra, obtained with the Ber
keley EUV/FUV spectrometer on the ORFEUS telescope in 1993 September,
have a resolution of 3000 and statistical signal-to-noise ratios betwe
en 20 and 80. We determine column densities for each observed rotation
al level and derive excitation temperatures and densities for the H-2
clouds along each line of sight. Our data continue the relationships a
mong H-2 column density, fractional molecular abundance, and reddening
apparent in Copernicus observations of nearby stars, indicating a com
mon mechanism for H-2 production. Estimates of cloud temperatures and
densities are consistent with those derived from Copernicus data. The
molecular fraction f is nearly constant over a wide range of distances
and mean reddenings, consistent with a model in which a significant f
raction of the neutral ISM is associated with H-2-bearing molecular cl
ouds, even along low-density lines of sight.