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We report the first detection of molecular hydrogen (H$_{2}$) absorption inthe Lyman-$\alpha$ emission line profiles of two classical T Tauri stars(CTTSs), DF Tau and V4046 Sgr, observed by \emph{HST}/COS. This absorption isthe energy source for many of the Lyman-band H$_{2}$ fluorescent lines commonlyseen in the far-ultraviolet spectra of CTTSs. We find that the absorbed energyin the H$_{2}$ pumping transitions from a portion of the Lyman-$\alpha$ linesignificantly differ from the amount of energy in the resulting fluorescentemission. By assuming additional absorption in the H I Lyman-$\alpha$ profilealong our light of sight, we can correct the H$_{2}$ absorption/emission ratiosso that they are close to unity. The required H I absorption for DF Tau is at avelocity close to the radial velocity of the star, consistent with H Iabsorption in the edge-on disk and interstellar medium. For V4046 Sgr, a nearlyface-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 thestar.

HST/COS Spectra of DF Tau and V4046 SGR: First Detection of Molecular Hydrogen Absorption Against the Ly$\alpha$ Emission Line