We report observations of the J =(1--0) C18O molecular emission line toward the L977 molecular cloud. To study the correlation between C18O emission and dust extinction we constructed a Gaussian smoothed map of the infrared extinction measured by Alves et al. (1998) at the same angular resolution (50) as our molecular--line observations. This enabled a direct comparison of C18O integrated intensities and column densities with dust extinction over a relatively large range of cloud depth (2 < Av < 30 mag) at 240 positions inside L977. We find a good linear correlation between these two column density tracers for cloud depths corresponding to Av < ~10 magnitudes. For cloud depths above this threshold there is a notable break in the linear correlation. Although either optically thick C18O emission or extremely low (Tex < 5 K) excitation temperatures at high extinctions could produce this departure from linearity, CO depletion in the denser, coldest regions of L977 may be the most likely cause of the break in the observed correlation. We directly derive the C18O abundance in this cloud over a broad range of cloud depths and find it to be virtually the same as that derived for IC 5146 from the data of Lada et al. (1994). In regions of very high extinction (Av > 10 mag), such as dense cores, our results suggest that C18O would be a very poor tracer of mass. Consequently, using C18O as a column density tracer in molecular clouds can lead to a 10 to 30% underestimation of overall cloud mass. We estimate the minimum total column density required to shield C18O from the interstellar radiation field to be 1.6 +/- 0.5 magnitudes of visual extinction.
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