Far-infrared lines of [N III] (57 mu m), [O III] (52, 88 mu m), [Ne II
I] (36 mu m), and [S III] (19, 33 mu m) have been measured in the H II
regions G1.13-0.11, W31B, G23.95+0.15, G25.38-0.18, G29.96-0.02, W43,
W51e, S156, S158, NGC 3576, NGC 3603, and G298.22-0.34. These observa
tions were made with the facility Cryogenic Grating Spectrometer on th
e Kuiper Airborne Observatory to examine variations in abundances thro
ughout the Galaxy. Previously published observations of G0.095+0.012,
G333.60-0.21, G45.13+0.14A, K3-50, and M17 are also discussed. The gia
nt H II region 30 Doradus in the Large Magellanic Cloud was observed f
or comparison. Fluxes for [Ne II] (12.8 mu m), [S IV] (10.5 mu m), and
the radio free-free continuum were collected from the literature for
these sources. Electron densities were estimated from FIR line-pair ra
tios, and ionic abundances were estimated from the FIR line and radio
fluxes. The excitation was estimated from the O++/S++ ratio. Correctio
ns for unseen ionization stages were calculated with the use of consta
nt-density H II region models. The validity and range of applicability
of such semiempirical ionization correction schemes are discussed. Th
e abundances with respect to hydrogen exhibit gradients with R(G) comp
arable to those previously measured for our Galaxy and for other galax
ies. The overall gradients are d (log N/H)/dR = -0.10 +/- 0.02 dex kpc
(-1), d (log Ne/H)/dR = -0.08 +/- 0.02 dex kpc(-1), and d (log S/H)/dR
-0.07 +/- 0.02 dex kpc(-1). Compared to the Orion Nebula, the interme
diate R(G) H II, regions with 6 < R(G) < 11 kpc have similar or lower
S/H and N/O ratios. The N/O ratios in the inner Galaxy are more than t
wice those observed in the Orion Nebula and intermediate R(G) H II reg
ions. In fact, all the abundance ratios are as well or better fitted b
y a step fit with two levels than by a linear gradient. This is best e
xhibited by N/O: N/O = 0.32 +/- 0.02 for R(G) less than or equal to 6
kpc and N/O = 0.18 +/- 0.01 for 6.4 < R(G) < 10.2 kpc. The lowest N/O
ratio (0.059 +/- 0.003) is found in 30 Doradus. As has been noted in p
revious studies, the N/O ratio estimated from infrared observations of
the doubly ionized N and O lines in H II regions is larger than the r
atio estimated from optical observations of the singly ionized N and O
lines. The excitation, as shown by the O++/S++ ratio, also varies wit
h R(G). Even though the H II regions were generally selected for high
ionization on the basis of high He+/H+ radio recombination line ratios
, the inner Galaxy H II regions all have low ionization (i.e., the oxy
gen and neon are mostly singly ionized), probably because they have hi
gher abundances. The Ne++/O++ ratio is observed to be essentially cons
tant over a wide range of excitation. This contradicts predictions of
model H II regions calculated with the use of LTE model stellar atmosp
heres. We conclude that these stellar atmospheres significantly undere
stimate the actual emergent fluxes for energies >41 eV.