  The excitement following the initial report of supersolid behavior for $^4$He
embedded in porous Vycor glass has been tempered by the realization that many
of the early supersolid observations were contaminated by effects arising from
an anomaly in the elastic properties of solid $^4$He. In an attempt to separate
dynamic elastic effects from a true supersolid signal, we employed a torsional
oscillator with two eigen frequencies to study the $^4$He-Vycor system. We
found that frequency dependent elastic signals can entirely account for the
observed period shift signals. Although, we conclude that supersolid does not
exist for the $^4$He-Vycor case, the question of its presence in bulk samples
remains open. In our current experiments we apply the two-frequency test to
bulk samples of solid $^4$He. Again we find a frequency dependent contribution
arising from elastic effects, however, in some cases we also find a small
frequency independent contribution, which may indicate the existence of a
remnant supersolid phase. Given the history of this subject such results must
be treated with caution.
