  We present H-alpha rotation curves of two low luminosity field galaxies with
r-band absolute magnitudes M_r=-13.9^{+0.8}_{-0.5} and M_r=-14.7^{+0.3}_{-0.2}
(for h=0.7; the large error bars reflect distance uncertainties). Most
previously studied galaxies in this luminosity range are members of groups
defined by brighter galaxies, but these two systems, selected from Blanton et
al.'s (2004) sample of low luminosity galaxies in the Sloan Digital Sky Survey
(SDSS), appear to have no bright companions. The measured rotation speeds at
the outer extent of the H-alpha rotation curves, 34.8+/-3.8 km/s and 30.9+/-7.2
km/s, are larger than the values of 16.0^{+6.1}_{-5.4} km/s and
20.9^{+6.2}_{-5.2} km/s predicted by extrapolating the inverse Tully-Fisher
relation of luminous SDSS galaxies to these faint luminosities. However, a
previous HI measurement of the first galaxy shows that it has a gas mass
similar to its stellar mass, and the total baryonic mass is consistent with
that predicted by McGaugh et al.'s (2000) "baryonic Tully-Fisher relation." We
find r-band dynamical mass-to-light ratios within the radii of the last H-alpha
data points (about 1.8 disk scale lengths in each case) of 12.6^{+4.7}_{-4.5}
Msun/Lsun and 4.8^{+2.5}_{-2.1} Msun/Lsun, much higher than the values ~ 1
Msun/Lsun expected for the stellar populations. The dynamical properties of
these galaxies, including the rotation speeds and evidence for high gas
fractions and dark matter domination within the luminous extent of the galaxy,
are consistent with those of previously studied faint galaxies in nearby
groups. Further studies of the SDSS sample will allow characterization of low
luminosity galaxies over the full range of environments in which they reside.
