  We report the first measurements of the branching fractions: $B(\psi(2S) ->
\gamma \eta') = (1.54 \pm 0.31 \pm 0.23) x 10^{-4}$ and $B(\psi(2S) -> \gamma
\eta) = (0.53 \pm 0.31 \pm 0.08) x 10^{-4}$. The $\psi(2S)$ to $\gamma \eta'$
result is consistent with expectations of a model that considers the
possibility of $\eta' - \eta$ mixing. The ratio of the $\psi(2S)$ to $\gamma
\eta'$ and $\psi(2S)$ to $\gamma \eta$ rates is used to determine the
pseudoscalar octet-singlet mixing angle.
