  We report the discovery of the second and third pulsating extremely low mass
white dwarfs (WDs), SDSS J111215.82+111745.0 (hereafter J1112) and SDSS
J151826.68+065813.2 (hereafter J1518). Both have masses < 0.25 Msun and
effective temperatures below 10,000 K, establishing these putatively He-core
WDs as a cooler class of pulsating hydrogen-atmosphere WDs (DAVs, or ZZ Ceti
stars). The short-period pulsations evidenced in the light curve of J1112 may
also represent the first observation of acoustic (p-mode) pulsations in any WD,
which provide an exciting opportunity to probe this WD in a complimentary way
compared to the long-period g-modes also present. J1112 is a Teff = 9590 +/-
140 K and log(g) = 6.36 +/- 0.06 WD. The star displays sinusoidal variability
at five distinct periodicities between 1792-2855 s. In this star we also see
short-period variability, strongest at 134.3 s, well short of expected g-modes
for such a low-mass WD. The other new pulsating WD, J1518, is a Teff = 9900 +/-
140 K and log(g) = 6.80 +/- 0.05 WD. The light curve of J1518 is highly
non-sinusoidal, with at least seven significant periods between 1335-3848 s.
Consistent with the expectation that ELM WDs must be formed in binaries, these
two new pulsating He-core WDs, in addition to the prototype SDSS
J184037.78+642312.3, have close companions. However, the observed variability
is inconsistent with tidally induced pulsations and is so far best explained by
the same hydrogen partial-ionization driving mechanism at work in classic
C/O-core ZZ Ceti stars.
