  We report a detailed spectral analysis of the population of low-mass X-ray
binaries (LMXBs) detected in the elliptical galaxy NGC~4278 with Chandra. Seven
luminous sources were studied individually, four in globular clusters (GCs),
and three in the stellar field. The range of (0.3-8 keV) $L_X$ for these
sources suggests that they may be black hole binaries (BHBs). Comparison of our
results with simulations allows us to discriminate between disk and power-law
dominated emission, pointing to spectral/luminosity variability, reminiscent of
Galactic BHBs. The BH masses derived from a comparison of our spectral results
with the $L_X \sim T^4_{in}$ relation of Galactic BHBs are in the 5-15
$M_{\odot}$ range, as observed in the Milky Way.
  The analysis of joint spectra of sources selected in three luminosity ranges
suggests that while the high luminosity sources have prominent thermal disk
emission components, power-law components are likely to be important in the mid
and low-luminosity spectra. Comparing low-luminosity average spectra, we find a
relatively larger $N_H$ in the GC spectrum; we speculate that this may point to
either a metallicity effect, or to intrinsic physical differences between field
and GC accreting binaries.
  Analysis of average sample properties uncover a previously unreported $L_X -
R_G$ correlation (where $R_G$ is the galactocentric radius) in the GC-LMXB
sample, implying richer LMXB populations in more central GCs. No such trend is
seen in the field LMXB sample. We can exclude that the GC $L_X - R_G$
correlation is the by-product of a luminosity effect, and suggest that it may
be related to the presence of more compact GCs at smaller galactocentric radii,
fostering more efficient binary formation.
