[en] Experimental observations have been made of the circulation of superfluid around a fine wire in a rotating container of He II. Measurements were made using a 25 μm diameter wire at temperatures slightly below 0.5 K and at rotation speeds in the range of +- 2.5 rad/sec. The important new result is the observation of stable reproducible levels of circulation at +-1.82 and +-2.73 quantum units. It is regarded as significant that these two levels, although not integral, are nevertheless multiples of the same scale factor 0.91. The origin of this scale factor has not been explained, but the fact that the stable levels scale at all is strong support for quantization