  We report the first detection of molecular hydrogen (H$_{2}$) absorption in
the Lyman-$\alpha$ emission line profiles of two classical T Tauri stars
(CTTSs), DF Tau and V4046 Sgr, observed by \emph{HST}/COS. This absorption is
the energy source for many of the Lyman-band H$_{2}$ fluorescent lines commonly
seen in the far-ultraviolet spectra of CTTSs. We find that the absorbed energy
in the H$_{2}$ pumping transitions from a portion of the Lyman-$\alpha$ line
significantly differ from the amount of energy in the resulting fluorescent
emission. By assuming additional absorption in the H I Lyman-$\alpha$ profile
along our light of sight, we can correct the H$_{2}$ absorption/emission ratios
so that they are close to unity. The required H I absorption for DF Tau is at a
velocity close to the radial velocity of the star, consistent with H I
absorption in the edge-on disk and interstellar medium. For V4046 Sgr, a nearly
face-on system, the required absorption is between +100 km/s and +290 km/s,
most likely resulting from H I gas in the accretion columns falling onto the
star.
