  We have constrained possible new interactions which produce nonrelativistic
potentials between polarized neutrons and unpolarized matter proportional to
$\alpha\vec{\sigma}\cdot\vec{v}$ where $\vec{\sigma}$ is the neutron spin and
$\vec{v}$ is the relative velocity. We use existing data from laboratory
measurements on the very long $T_{1}$ and $T_{2}$ spin relaxation times of
polarized $^{3}$He gas in glass cells.Using the best available measured $T_{2}$
of polarized $^{3}$He gas atoms as the polarized source and the earth as an
unpolarized source, we obtain constraints on two new interactions. We present a
new experimental upper bound on possible vector-axial-vector($V_{VA}$) type
interactions for ranges between $1\sim10^{8}$m. In combination with previous
results, we set the most stringent experiment limits on $g_{V}g_{A}$ ranging
from $\sim\mu$m to $\sim10^{8}$m. We also report what is to our knowledge the
first experimental upper limit on the possible torsion fields induced by the
earth on its surface. Dedicated experiments could further improve these bounds
by a factor of $\sim100$. Our method of analysis also makes it possible to
probe many velocity dependent interactions which depend on the spins of both
neutrons and other particles which have never been searched for before
experimentally.
