  We report the discovery of two new pulsating extremely low-mass (ELM) white
dwarfs (WDs), SDSS J161431.28+191219.4 (hereafter J1614) and SDSS
J222859.93+362359.6 (hereafter J2228). Both WDs have masses <0.25 Msun and thus
likely harbor helium cores. Spectral fits indicate these are the two coolest
pulsating WDs ever found. J1614 has Teff = 8880 +/- 170 K and log g = 6.66 +/-
0.14, which corresponds to a roughly 0.19 Msun WD. J2228 is considerably
cooler, with a Teff = 7870 +/- 120 K and log g = 6.03 +/- 0.08, which
corresponds to a roughly 0.16 Msun WD, making it the coolest and lowest-mass
pulsating WD known. There are multiple ELM WDs with effective temperatures
between the warmest and coolest known ELM pulsators that do not pulsate to
observable amplitudes, which questions the purity of the instability strip for
low-mass WDs. In contrast to the CO-core ZZ Ceti stars, which are believed to
represent a stage in the evolution of all such WDs, ELM WDs may not all evolve
as a simple cooling sequence through an instability strip. Both stars exhibit
long-period variability (1184-6235 s) consistent with non-radial g-mode
pulsations. Although ELM WDs are preferentially found in close binary systems,
both J1614 and J2228 do not exhibit significant radial-velocity variability,
and are perhaps in low-inclination systems or have low-mass companions. These
are the fourth and fifth pulsating ELM WDs known, all of which have
hydrogen-dominated atmospheres, establishing these objects as a new class of
pulsating WD.
