Far-infrared lines of [N III] (57 mu m), [O III] (52, 88 mu m), [Ne III] (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 observations were made with the facility Cryogenic Grating Spectrometer on the Kuiper Airborne Observatory to examine variations in abundances throughout 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 giant H II region 30 Doradus in the Large Magellanic Cloud was observed for 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 ratios, and ionic abundances were estimated from the FIR line and radio fluxes. The excitation was estimated from the O++/S++ ratio. Corrections for unseen ionization stages were calculated with the use of constant-density H II region models. The validity and range of applicability of such semiempirical ionization correction schemes are discussed. The abundances with respect to hydrogen exhibit gradients with R(G) comparable to those previously measured for our Galaxy and for other galaxies. 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 intermediate 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 twice those observed in the Orion Nebula and intermediate R(G) H II regions. In fact, all the abundance ratios are as well or better fitted by a step fit with two levels than by a linear gradient. This is best exhibited 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 previous 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 ratio estimated from optical observations of the singly ionized N and O lines. The excitation, as shown by the O++/S++ ratio, also varies with 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 oxygen and neon are mostly singly ionized), probably because they have higher abundances. The Ne++/O++ ratio is observed to be essentially constant over a wide range of excitation. This contradicts predictions of model H II regions calculated with the use of LTE model stellar atmospheres. We conclude that these stellar atmospheres significantly underestimate the actual emergent fluxes for energies >41 eV.
