Measurement of the Charge Asymmetry in the Decayη→π+π−π0

We have measured the charge asymmetry in the decay $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$. $\ensuremath{\eta}'\mathrm{s}$ were produced in the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\eta}n$ at 730 and 810 $\frac{\mathrm{MeV}}{c}$ incident pion momentum. We obtain an asymmetry of -0.0005 \ifmmode\pm\else\textpm\fi{} 0.0022 for 220 659 events. We see no evidence for $C$-invariance violation in this decay.