Higher-Order Corrections to the Large-$N_c$ Bound on $M_{\eta }\mathrm{/}{M}_{{\eta }^{\mathrm{\prime }}}$

Next-to-leading $1\mathrm{/}\mathbb{N}$ corrections to the upper bound on $M_{\eta}/M_{\eta '}$ recently obtained by Georgi are considered. These corrections are just what is needed to reconcile the bound with the observed $\eta$ and ${\eta }^{\mathrm{\prime }}$ masses.