High-precision electron scattering measurements from the 15.109-MeV ${1}^{+}$ state in $^{12}\mathrm{C}$ are made at $\ensuremath{\theta}=75 \mathrm{and} 110\ifmmode^\circ\else\textdegree\fi{}$ with $35\ensuremath{\le}E\ensuremath{\le}55$ MeV. From the measurements $B(M1)$ is extrapolated to the photon point and the radiative width is determined, ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}=37.0\ifmmode\pm\else\textpm\fi{}1.1$ eV. The corresponding weak magnetism results for $\ensuremath{\beta}$ decay and $\ensuremath{\mu}$ capture are given.
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