Polarization in. pi. /sup -/p elastic scattering at 1180, 1250, and 1360 MeV/c. [Scattering amplitudes]

We have measured the polarization parameter in ${\ensuremath{\pi}}^{\ensuremath{-}}p$ elastic scattering at laboratory momenta of 1180, 1250, and 1360 MeV/c in the angular interval $65\ifmmode^\circ\else\textdegree\fi{}l{\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}l115\ifmmode^\circ\else\textdegree\fi{}$. The results were used to show that the polarized target used in these (and other similar) experiments was uniformly polarized. These measurements were also used to resolve pre-existing experimental discrepancies in the determination of the polarization parameter, and to clarify the behavior of scattering amplitudes in this energy range. We show that local measurements of this type are important in resolving discrete ambiguities affecting the energy continuation of the amplitudes. An important by-product of this experiment is the development of a fast method of reconstructing particle trajectories and fitting the elastic events, which could have a significant impact for future high-statistics experiments.