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It is proposed to extend to the NAL energy range the investigation of elastic ''diffraction'' scattering and precision measurements of the total cross sections performed at BNL during the past decade. It is expected that this investigation will be of considerable interest and importance in regard to understanding the asymptotic behavior of forward and near forward scattering amplitudes. The investigation will be composed of two highly complementary parts, which in common utilize the same beam, most of the same equipment, and the same experimental area region. As our past experience has demonstrated, a knowledge of both the elastic ''diffraction'' scattering and the total cross sections to high precision is necessary to allow a meaningful theoretical analysis of either

Behavior of high energy elastic scattering and total cross sections for pi+/- p, k+/- p, pp and p - anti-p