  The carbon content of protoplanetary disks is an important parameter to
characterize planets formed at different disk radii. There is some evidence
from far-infrared and submillimeter observations that gas in the outer disk is
depleted in carbon, with a corresponding enhancement of carbon-rich ices at the
disk midplane. Observations of the carbon content inside of the inner
sublimation rim could confirm how much carbon remains locked in kilometer size
bodies in the disk. Using near-infrared spectra, I self-consistently determine
the stellar, extinction, veiling, and accretion properties of the 26 stars in
my sample. From these values, I extract the inner disk excess of the target
stars and identify a series of C^0 recombination lines in 18 of these disks and
use the CHIANTI atomic line database with an optically thin slab model to
constrain the average n_e, T_e, and n_C for these lines in the five disks with
a complete set of lines. By comparing these values with other slab models of
the inner disk using the Cloudy photoionization code, I also constrain n_H and
the carbon abundance, X_C, and hence the amount of carbon `missing' from the
slab. The inner disks are extremely dense (n_H~10^{16} cm^{-3}), warm (T_e~4500
K), and moderately ionized (logX_e~3.3). Three of the five modeled disks show
robust carbon depletion <=42 relative to the solar value. I discuss multiple
ways in which the `missing' carbon could be locked out of the accreting gas.
Given the high-density inner disk gas, evidence for radial drift, and lack of
obvious gaps in these three systems, their carbon depletion is most consistent
with the `missing' carbon being sequestered in kilometer size bodies. For DR
Tau, nitrogen and silicon are also depleted by factors of 45 and 4,
respectively, suggesting that the kilometer size bodies into which the grains
are locked were formed beyond the N_2 snowline.
