In order to determine molecular fractional abundances, both the molecular density and hydrogen density must be known. In this study we have determined these parameters by fitting the observed intensities of J = 2 → 1 and J = 1 → 0 13CO and C18O transitions using a spherical cloud LVG radiative transfer model. The kinetic temperature is determined by observations of 12CO and is found to be between 9 K and 13 K for our sources. The fractional abundance of CO is expected to rise rapidly between regions of low extinction and those with Av ≥ 4 mag, due primarily to the decrease in photodestruction rates (Langer 1976). The C18O fractional abundance data plotted as function of Av support a nonlinear relationship between X(C18O) and Av for Av ≤ 4 mag, with an indication of an asymptotoic value X(C18O) = 2.2 × 10 (-7) in highly obscured regions. For 16O/18O ratios of 250 (suggested by our data although possible uncorrected saturation of 13CO makes this a lower limit) and 700 (A. Penzias, private communication) the fractions of carbon in CO in well-shielded regions are .08 and .23, respectively.