Surface Contour of Rotating Liquid Helium II

The curvature of the free surface of a thin layer of liquid helium II resting on the horizontal bottom of a rotating cylindrical container (radius=1.26 cm) was measured by a sensitive optical method. For a liquid depth of $h=5.0\mathrm{}\times {10}^{-3\mathrm{}}$ cm and $T=1.11\mathrm{}$°K, the steady-state curvature was found to be indistinguishable from that of an ordinary viscous liquid for rotational speeds down to $\omega =0.29\mathrm{}$ rad/sec. Transient effects were observed which differ qualitatively from those of a normal viscous liquid. These results are discussed in relation to various theories of rotating helium and are compared with other measurements.