  A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep
1998)] to measure the noncyclic phase associated with a precessing neutron spin
in a neutron interferometer, as given by the Pancharatnam criterion, is
presented. It is pointed out that since the experiment measures, not the
noncyclic phase itself, but a quantity derived from it, it misses the most
interesting feature of such a phase, namely the different sign associated with
states lying in the upper and the lower hemispheres, a feature originating in
the existence of a phase singularity. Such effects have earlier been predicted
and seen in optical interference experiments using polarization of light as the
spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].
