  We present Herschel observations of six fine-structure lines in 25
Ultraluminous Infrared Galaxies at z<0.27. The lines, [O III]52, [N III]57, [O
I]63, [N II]122, [O I]145, and [C II]158, are mostly single gaussians with
widths <600 km s-1 and luminosities of 10^7 - 10^9 Solar. There are deficits in
the [O I]63/L_IR, [N II]/L_IR, [O I]145/L_IR, and [C II]/L_IR ratios compared
to lower luminosity systems. The majority of the line deficits are consistent
with dustier H II regions, but part of the [C II] deficit may arise from an
additional mechanism, plausibly charged dust grains. This is consistent with
some of the [C II] originating from PDRs or the ISM. We derive relations
between far-IR line luminosities and both IR luminosity and star formation
rate. We find that [N II] and both [O I] lines are good tracers of IR
luminosity and star formation rate. In contrast, [C II] is a poor tracer of IR
luminosity and star formation rate, and does not improve as a tracer of either
quantity if the [C II] deficit is accounted for. The continuum luminosity
densities also correlate with IR luminosity and star formation rate. We derive
ranges for the gas density and ultraviolet radiation intensity of 10^1 < n <
10^2.5 and 10^2.2 < G_0 < 10^3.6, respectively. These ranges depend on optical
type, the importance of star formation, and merger stage. We do not find
relationships between far-IR line properties and several other parameters; AGN
activity, merger stage, mid-IR excitation, and SMBH mass. We conclude that
these far-IR lines arise from gas heated by starlight, and that they are not
strongly influenced by AGN activity.
