We report our measurements of the cross sections ${\ensuremath{\sigma}}_{5S}$ and ${\ensuremath{\sigma}}_{4D}$ for the electronic-energy-transfer process $\mathrm{Na}(3P)+\mathrm{Na}(3P)\ensuremath{\rightarrow}\mathrm{Na}(5S,4D)+\mathrm{Na}(3S)$. To obtain these cross sections we have measured the fluorescence intensity for the transitions $5S\ensuremath{\rightarrow}3P$, $4D\ensuremath{\rightarrow}3P$, and $3P\ensuremath{\rightarrow}3S$ in sodium vapor excited with a cw dye laser. The study of this electronic energy transfer is complicated and there is a large disagreement (\ensuremath{\gtrsim}
104) among reported measurements. We believe we have avoided most of the difficulties of previous experiments. Our results are ${\ensuremath{\sigma}}_{5S}=(2.0\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$
cm2 and ${\ensuremath{\sigma}}_{4D}=(3.2\ifmmode\pm\else\textpm\fi{}1.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{\ensuremath{-}2}$, and they are compared with the results of other experiments.