It is suggested that the property of nonclassical rotational inertia possessed by superfluid liquid helium may be shared by some solids. In particular, nonclassical rotational inertia very probably occurs if the solid is Bose-condensed as recently proposed by Chester. Anomalous macroscopic effects are then predicted. However, the associated superfluid fraction is shown to be very small (probably 10^-4) even at $T=0$, so that these effects could well have been missed. Direct tests are proposed.
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A. J. Leggett (1970) studied this question.
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