  We have observed emission lines of [S IV] 10.51, H(7-6) 12.37, [Ne II] 12.81,
[Ne III] 15.56, and [S III] 18.71 um in a number of extragalactic H II regions
with the Spitzer Space Telescope. A previous paper presented our data and
analysis for the substantially face-on spiral galaxy M83. Here we report our
results for the local group spiral galaxy M33. The nebulae selected cover a
wide range of galactocentric radii (R_G). The observations were made with the
Infrared Spectrograph with the short wavelength, high resolution module. The
above set of five lines is observed cospatially, thus permitting a reliable
comparison of the fluxes. From the measured fluxes, we determine the ionic
abundance ratios including Ne++/Ne+, S3+/S++, and S++/Ne+ and find that there
is a correlation of increasingly higher ionization with larger R_G. By sampling
the dominant ionization states of Ne (Ne+, Ne++) and S (S++, S3+) for H II
regions, we can estimate the Ne/H, S/H, and Ne/S ratios. We find from linear
least-squares fits that there is a decrease in metallicity with increasing R_G:
d log (Ne/H)/dR_G = -0.058+-0.014 and d log (S/H)/dR_G = -0.052+-0.021 dex
kpc-1. There is no apparent variation in the Ne/S ratio with R_G. Unlike our
previous similar study of M83, where we conjectured that this ratio was an
upper limit, for M33 the derived ratios are likely a robust indication of Ne/S.
This occurs because the H II regions have lower metallicity and higher
ionization than those in M83. Both Ne and S are primary elements produced in
alpha-chain reactions, following C and O burning in stars, making their yields
depend very little on the stellar metallicity. Thus, it is expected that Ne/S
remains relatively constant throughout a galaxy. The median (average) Ne/S
ratio derived for H II regions in M33 is 16.3 (16.9), just slightly higher than
