Relative decay rates of eta ---> pi+ pi- pi0, eta ---> pi+ pi- gamma, eta ---> pi+ pi- pi0 gamma, and eta ---> pi+ pi-

We have measured the branching ratio (η→π+π−γ)(η→π+π−π0) to be 0.209±0.004. The rare decays η→π+π−π0γ and η→π+π− were searched for and not found. The upper limit on the branching ratio (η→π+π−π0γ)(η→π+π−π0) is 0.0024 at 90% confidence level, and the upper limit on the width of the decay η→π+π− is 4 eV. We then have a limit on the rate of a P- and T-violating strong interaction: Rate (P−and T−violatingstronginteraction)Rate (conventionalstronginteraction)<4×10−8.