The far-ultraviolet spectra of HD 219188, HD 94473, and HD 18100, three ear
ly-type stars in the Galactic halo, were obtained with the echelle spectrom
eter on the ORFEUS II telescope in 1996 November. We derive H-2 column dens
ities for the rotational levels up to J " = 6 and estimate excitation tempe
ratures and H-2 dissociation rates for the clouds toward HD 219188 and HD 9
4473. The results indicate that strong radiation fields might exist near th
ese clouds, but these radiation fields do not seem to act as major heating
sources. No significant H-2 absorption is seen toward HD 18100. The correla
tion between our H-2 column densities and published extinction maps confirm
s that the molecular clouds are associated with dust clouds that lie betwee
n the observed stars and the Sun. We estimate the conversion factor between
N(H-2) and W((CO)-C-12) to be X-CO = 4 +/- 2 x 10(19) cm(-2) (K km s(-1))(
-1) for the clouds along the line of sight to HD 94473, consistent with pre
vious estimates to within a factor of a few.