  We have studied the thermal history of the resonant frequency of a torsional
oscillator containing solid 4He. We find that the magnitude of the frequency
shift that occurs below 100 mK is multivalued in the low temperature limit,
with the exact value depending on how the state is prepared. This result can be
qualitatively explained in terms of the motion and pinning of quantized
vortices within the sample. Several aspects of the data are also consistent
with the response of dislocation lines to oscillating stress fields imposed on
the solid.
