  Neutron spin rotation is expected from quark-quark weak interactions in the
Standard Model, which induce weak interactions among nucleons that violate
parity. We present the results from an experiment searching for the effect of
parity violation via the spin rotation of polarized neutrons in a liquid
$^{4}$He medium. The value for the neutron spin rotation angle per unit length
in $^{4}$He, $d\phi/dz =(+2.1 \pm 8.3 (stat.) \pm 2.9 (sys.))\times10^{-7}$
rad/m, is consistent with zero. The result agrees with the best current
theoretical estimates of the size of nucleon-nucleon weak amplitudes from other
experiments and with the expectations from recent theoretical approaches to
weak nucleon-nucleon interactions. In this paper we review the theoretical
status of parity violation in the $\vec{n}+^{4}$He system and discuss details
of the data analysis leading to the quoted result. Analysis tools are presented
that quantify systematic uncertainties in this measurement and that are
expected to be essential for future measurements.
