  We discuss the interstellar absorption from many atomic and molecular species
seen in high-resolution $HST$/STIS UV and high-S/N optical spectra of the
moderately reddened B3-5~V star HD~62542. This remarkable sight line exhibits
both very steep far-UV extinction and a high fraction of hydrogen in molecular
form -- with strong absorption from CH, C$_2$, CN, and CO, but weak absorption
from CH$^+$ and most of the commonly observed diffuse interstellar bands. Most
of the material resides in a single narrow velocity component -- offering a
rare opportunity to probe the primarily molecular core of a single interstellar
cloud with little associated diffuse atomic gas. Detailed analyses of the
spectra indicate that: (1) the molecular fraction in the main cloud is high
[$f$(H$_2$) $>$ 0.8]; (2) the gas is fairly cold ($T_{\rm k}$ = 40--43 K, from
the rotational excitation of H$_2$ and C$_2$); (3) the local hydrogen density
$n_{\rm H}$ $\sim$ 1500 cm$^{-3}$ (from the C$_2$ excitation, the
fine-structure excitation of C$^0$, and simple chemical models); (4) the
unusually high excitation temperatures for $^{12}$CO and $^{13}$CO may be
largely due to radiative excitation; (5) $N$(C$^+$):$N$(CO):$N$(C) $\sim$
100:10:1; (6) the depletions of many elements are more severe than those seen
in any other sight line, and the detailed pattern of depletions differs from
those derived from larger samples of Galactic sight lines; and (7) the various
neutral/first ion ratios do not yield consistent estimates for the electron
density, even when the effects of grain-assisted recombination and
low-temperaure dielectronic recombination are considered.
