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Measurements of gas mass in protoplanetary gas disks form the basis forestimating the conditions of planet formation. Among the most importantconstraints derived from disk diagnostics are the abundances of gas-phasespecies critical for understanding disk chemistry. Towards this end, we presentdirect line-of-sight measurements of H$_{2}$ and CO, employing UV absorptionspectroscopy from $HST$-COS to characterize disk composition, molecularexcitation temperatures, and spatial distribution in the circumstellar materialaround the Herbig Ae stars HK Ori and T Ori. We observe strong CO (N(CO) =10$^{15.5}$ cm$^{-2}$; T$_{rot}$(CO) = 19 K) and H$_{2}$ (N(H$_{2}$) =10$^{20.34}$ cm$^{-2}$; T$_{rot}$(H$_{2}$) = 141 K) absorption towards HK Oriwith a CO/H$_{2}$ ratio ($\equiv$ N(CO)/N(H$_{2}$)) =1.3$^{+1.6}_{-0.7}$~$\times$~10$^{-5}$. These measurements place directempirical constraints on the CO-to-H$_{2}$ conversion factor in the disk arounda Herbig Ae star for the first time, although there is uncertainty concerningthe exact viewing geometry of the disk. The spectra of T Ori show CO (N(CO) =10$^{14.9}$ cm$^{-2}$; T$_{rot}$(CO) = 124 K) absorption. Interestingly, we donot detect any H$_{2}$ absorption towards this star (N(H$_{2}$) $<$ 10$^{15.9}$cm$^{-2}$). We discuss a potential scenario for the detection of CO withoutH$_{2}$, which deserves further investigation. The low abundance ratio measuredaround HK Ori suggests significant depletion of CO in the circumstellar gas,which conforms with the handful of other recent CO abundance measurements inprotoplanetary disks.

A CO-to-H$_2$ ratio of $\approx 10^{-5}$ towards the Herbig Ae star HK Ori