  We report a measurement of two energy-weighted gamma cascade angular
distributions from polarized slow neutron capture on the ${}^{35}$Cl nucleus,
one parity-odd correlation proportional to $\vec{s_{n}} \cdot \vec{k_{\gamma}}$
and one parity-even correlation proportional to $\vec{s_{n}} \cdot \vec{k_{n}}
\times \vec{k_{\gamma}}$. A parity violating asymmetry can appear in this
reaction due to the weak nucleon-nucleon (NN) interaction which mixes opposite
parity S and P-wave levels in the excited compound $^{36}$Cl nucleus formed
upon slow neutron capture. If parity-violating (PV) and parity-conserving (PC)
terms both exist, the measured differential cross section can be related to
them via $\frac{d\sigma}{d\Omega}\propto1+A_{\gamma,
PV}\cos\theta+A_{\gamma,PC}\sin\theta$. The PV and PC asymmetries for
energy-weighted gamma cascade angular distributions for polarized slow neutron
capture on $^{35}$Cl averaged over the neutron energies from 2.27~meV to
9.53~meV were measured to be $A_{\gamma,PV}=(-23.9\pm0.7)\times 10^{-6}$ and
$A_{\gamma,PC}=(0.1\pm0.7)\times 10^{-6}$. These results are consistent with
previous experimental results. Systematic errors were quantified and shown to
be small compared to the statistical error. These asymmetries in the angular
distributions of the gamma rays emitted from the capture of polarized neutrons
in $^{35}$Cl were used to verify the operation and data analysis procedures for
the NPDGamma experiment which measured the parity-odd asymmetry in the angular
distribution of gammas from polarized slow neutron capture on protons.
