  To investigate the relative amount of ejecta from high-mass versus
intermediate-mass stars and to trace the chemical evolution of the Galaxy, we
have performed with the IRAM 30m and the SMT 10m telescopes a systematic study
of Galactic interstellar 18O/17O ratios toward a sample of 421 molecular
clouds, covering a galactocentric distance range of 1-22 kpc. The results
presented in this paper are based on the J=2-1 transition and encompass 364
sources showing both C18O and C17O detections. The previously suggested 18O/17O
gradient is confirmed. For the 41 sources detected with both facilities, good
agreement is obtained. A correlation of 18O/17O ratios with heliocentric
distance is not found, indicating that beam dilution and linear beam sizes are
not relevant. For the subsample of IRAM 30 m high-mass star-forming regions
with accurate parallax distances, an unweighted fit gives 18O/17O =
(0.12+-0.02)R_GC+(2.38+-0.13) with a correlation coefficient of R = 0.67. While
the slope is consistent with our J=1-0 measurement, ratios are systematically
lower. This should be caused by larger optical depths of C18O 2-1 lines, w.r.t
the corresponding 1-0 transitions, which is supported by RADEX calculations and
the fact that C18O/C17O is positively correlated with 13CO/C18O. After
considering optical depth effects with C18O J=2-1 reaching typically an optical
depth of 0.5, corrected 18O/17O ratios from the J=1-0 and J=2-1 lines become
consistent. A good numerical fit to the data is provided by the MWG-12 model,
including both rotating stars and novae.
