The differential cross section and the polarization from the elastic scattering of 40-MeV protons were measured for

{}^{12}C

{}^{40}{Ca}

{}^{58}{Ni}

{}^{90}{Zr}

, and

{}^{208}{Pb}

. The polarized proton beam was obtained in two ways: (a) by scattering hydrogen from 80-MeV

α

particles, which gave (89±7)% polarization at an intensity of 2×

10^{7}

p/sec; and (b) by elastic scattering of protons from Ca, resulting in (35±3)% polarization and an intensity of 1.5×

10^{8}

p/sec. A 32-NaI(TI)-detector array was used to measure the scattering at 10° intervals simultaneously. In addition to the elastic-scattering and polarization measurements given above, we also obtained the differential cross section and polarization for inelastic scattering from the 4.43-MeV state in

{}^{12}C

, and the differential cross sections alone for the 7.66- and 9.63-MeV states. Optical-model calculations were made in such a way that simultaneous fits to the polarization and the differential cross section were obtained. An 11-parameter "best fit" search was made on each target, as well as an "average geometry" search where the geometric parameters were fixed and only the depths of the potentials allowed to vary. From the optical-model calculations we conclude that (1) the radius of the spin-orbit potential is smaller than that for the real potential, (2) for nuclei heavier than Ca, surface absorption alone gives a poorer fir than a combination of volume and surface absorption, and (3) the increase in well depth with

A

indicates the presence of a nuclear symmetry term in the real potential.

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