Study of gluon versus quark fragmentation in ${\rm Y}\to \mathrm{gg}\gamma$ and $e^{+}{e}^{-}\to q\overline{q}\gamma$ events at $\sqrt{s}$=10 GeV

Using data collected with the CLEO II detector at the Cornell Electron Storage Ring, we determine the ratio $R_{\mathrm{chrg}}$ for the mean charged multiplicity observed in ${\rm Y}\mathrm{}\left(1S\right)\mathrm{}\to \mathrm{gg}\gamma$ events, $〈n_{\mathrm{gluon}}^{\pm }〉$, to the mean charged multiplicity observed in $e^{+}{e}^{-}\to q\overline{q}\gamma$ events, $〈n_{\mathrm{quark}}^{\pm }〉$. We find $R_{\mathrm{chrg}}\equiv 〈n_{\mathrm{gluon}}^{\pm }〉/〈n_{\mathrm{quark}}^{\pm }〉=1.04\mathrm{}$ $\pm 0.02\left(\mathrm{stat}\right)\pm 0.05\left(\mathrm{syst}\right)$ for jet-jet masses less than 7 GeV.