A search has been made for pion-pion resonances in the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}+{\ensuremath{\pi}}^{0}+p$ at incident pion energies of 871 Mev and 775 Mev, using a sodium-iodide luminescent chamber as a detector. The spectra of ${m}^{*}$, the total energy of the two pions in their own barycentric system, are presented and compared with the spectra predicted by phase-space alone. The maximum ${m}^{*}$ which can be obtained in this experiment is 695 Mev and the recoil proton momenta range from 400 to 700 Mev/c. The 871-Mev spectrum shows a deviation from the phase-space prediction in the form of an abrupt rise at an ${m}^{*}$ of 590 Mev. This rise is most prominent for the spectrum with recoil proton momenta above 550 Mev/c. The 775-Mev spectrum does not show any strong deviations from phase space. It is concluded, on the basis of this experiment and other experiments at similar or somewhat higher-incident pion energies, that the peak above phase space in the ${m}^{*}$ spectrum range of 575 to 700 Mev is due to at least one other process besides the 765-Mev two-pion resonance particular. The possible existence of a new two-pion, $T=1$ resonance with an ${m}^{*}$ of about 600 Mev is discussed. An evaluation of the performance of the luminescent chamber in this experiment is made.