  Measurements of gas mass in protoplanetary gas disks form the basis for
estimating the conditions of planet formation. Among the most important
constraints derived from disk diagnostics are the abundances of gas-phase
species critical for understanding disk chemistry. Towards this end, we present
direct line-of-sight measurements of H$_{2}$ and CO, employing UV absorption
spectroscopy from $HST$-COS to characterize disk composition, molecular
excitation temperatures, and spatial distribution in the circumstellar material
around 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 Ori
with a CO/H$_{2}$ ratio ($\equiv$ N(CO)/N(H$_{2}$)) =
1.3$^{+1.6}_{-0.7}$~$\times$~10$^{-5}$. These measurements place direct
empirical constraints on the CO-to-H$_{2}$ conversion factor in the disk around
a Herbig Ae star for the first time, although there is uncertainty concerning
the 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 do
not 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 without
H$_{2}$, which deserves further investigation. The low abundance ratio measured
around HK Ori suggests significant depletion of CO in the circumstellar gas,
which conforms with the handful of other recent CO abundance measurements in
protoplanetary disks.
