Study of the reaction<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>→</mml:mo><mml:mi>γ</mml:mi><mml:mi>γ</mml:mi><mml:mfrac><mml:mrow><mml:mi>J</mml:mi></mml:mrow><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow></mml:mfrac></mml:math>

The Crystal Ball detector at SPEAR has been used to investigate the decays ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}\frac{J}{\ensuremath{\psi}}$, $\frac{J}{\ensuremath{\psi}}\ensuremath{\rightarrow}({e}^{+}{e}^{\ensuremath{-}} or {\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$ resulting from production of $8\ifmmode\times\else\texttimes\fi{}{10}^{5}{\ensuremath{\psi}}^{\ensuremath{'}}$. From this selection of the data we measure the branching ratios for the processes ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}(\ensuremath{\eta} or {\ensuremath{\pi}}^{0})\frac{J}{\ensuremath{\psi}}$ and ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\chi}$, $\ensuremath{\chi}\ensuremath{\rightarrow}\ensuremath{\gamma}\frac{J}{\ensuremath{\psi}}$. An analysis of the angular correlations in the latter process furnishes measurements of the $\ensuremath{\chi}(3.55)$ and $\ensuremath{\chi}(3.51)$ spins and of the multipole structure of the radiative transitions.