be expressed by: $$\begin{aligned}
f_{\rm D} & = & x({\rm CO})_{\rm can} \times 
    \frac{N(\MOLH )_{\rm 1.2mm}}{N(\CEIO )} 
    \frac{[\rm ^{18}O]}{[\rm ^{16}O]} \nonumber \\
          & = & 8.5\times 10^{-2} 
    \frac{{\cal F}_{{\rm 1.2mm}}({\rm mJy/22\sec beam})}
    {W_{\CEIO}({\rm K \, km \, s^{-1}})} 
     \label{efd}.\end{aligned}$$ To derive eq. (\[efd\]) we have assumed a dust temperature $T_{\rm dust}$ = 10 K, $\kappa_{\rm 1.2mm}$ = 0.005 cm$^2$ g$^{-1}$, and an abundance ratio $[\rm ^{16}O]/[\rm ^{18}O]$ = 560 (Wilson & Rood [@wr94]).

There are several [*caveats*]{} to the above procedure. One is that the “canonical abundance” appears to vary from cloud to cloud (Lacy et al. [@lkg94]; Alves et al. [@all99]; Kramer et al. [@kra99]) and is roughly one third of the diffuse cloud carbon gas phase abundance (Sofia et al. [@scg97]). Given that CO is expected to represent essentially all the gas phase carbon in molecular clouds, this suggests depletion of carbon in some form (not necessarily as solid CO) even on the outskirts of cores (we note that the direct study of CO solid state features in Taurus (Chiar et al. [@cak95]) shows that solid CO towards 4 field stars in Taurus is less than 40%  of the canonical gas phase CO abundance and is observed for 