We have measured the moment of inertia of hcp ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ crystals from 25 mK to 2 K. With a precision of five parts in ${10}^6$ we find no evidence for a nonclassical rotational inertia. This indicates that if a supersolid exists, it has a $\frac{{\rho }_s}{\rho }$ of less than 5 × ${10}^{-6\mathrm{}}$, a transition temperature of less than 25 mK, or a critical velocity of less than 5 μm/sec.

• Received 10 April 1981

DOI:https://doi.org/10.1103/PhysRevB.24.2844