  The NEWS-G collaboration uses Spherical Proportional Counters (SPCs) to
search for weakly interacting massive particles (WIMPs). In this paper, we
report the first measurements of the nuclear quenching factor in neon gas at
\SI{2}{bar} using an SPC deployed in a neutron beam at the TUNL facility. The
energy-dependence of the nuclear quenching factor is modelled using a simple
power law: $\alpha$E$_{nr}^{\beta}$; we determine its parameters by
simultaneously fitting the data collected with the detector over a range of
energies. We measured the following parameters in Ne:CH$_{4}$ at \SI{2}{bar}:
$\alpha$ = 0.2801 $\pm$ 0.0050 (fit) $\pm$ 0.0045 (sys) and $\beta$ = 0.0867
$\pm$ 0.020 (fit) $\pm$ 0.006(sys). Our measurements do not agree with expected
values from SRIM or Lindhard theory. We demonstrated the feasibility of
performing quenching factor measurements at sub-keV energies in gases using
SPCs and a neutron beam.
