  The non-divergent diagrams describing two-gluon exchange and annihilation
between quarks and antiquarks are calculated in the Feynman gauge, based on
quantum chromodynamics in a spherical cavity. Using the experimental $N$,
$\Delta$, $\Omega$, and $\rho$ masses to fit the free parameters of the M.I.T.\
bag model, the predicted states agree very well with the observed low-lying
hadrons. As expected, the two-gluon annihilation graphs lift the degeneracy of
the $\pi$ and $\eta$, while the $\rho$ and $\omega$ remain degenerate.
Diagonalizing the $\eta - \eta'$ subspace Hamiltonian yields a very good value
for the mass of the $\eta$ meson.
