We present detailed analyses of the absorption spectrum seen in QSO 2359 -
1241 (NVSS J235953 - 124148). Keck HIRES data reveal absorption from 20 tra
nsitions arising from He I, Mg I, Mg II, Ca II, and Fe II. Hubble Space Tel
escope data show broad absorption lines (BALs) from Al III lambda 1857, C I
V lambda 1549, Si IV lambda 1397, and N V lambda 1240. Absorption from exci
ted Fe II states constrains the temperature of the absorber to 2000 less th
an or similar to T less than or similar to 10,000 K and puts a lower limit
of 10(5) cm(-3) on the electron number density. Saturation diagnostics show
that the real column densities of He I and Fe II can be determined, allowi
ng us to derive meaningful constraints on the ionization equilibrium and ab
undances in the flow. The ionization parameter is constrained by the iron,
helium, and magnesium data to -3.0 less than or similar to log (U) less tha
n or similar to -2.5, and the observed column densities can be reproduced w
ithout assuming departure from solar abundances. From comparison of the He
I and Fe II absorption features, we infer that the outflow seen in QSO 2359
- 1241 is not shielded by a hydrogen ionization front and therefore that t
he existence of low-ionization species in the outflow (e.g., Mg II, Al III,
Fe II) does not necessitate the existence of such a front. We find that th
e velocity width of the absorption systematically increases as a function o
f ionization and to a lesser extent with abundance. Complementary analyses
of the radio and polarization properties of the object are discussed in a c
ompanion paper (Brotherton et al.).