The elastic scattering of C/sup 12/ ions from Ar, Fe, Ni, Ag/sup 107/ In, and Ta was measured as a function of angle, at a laboratory-system energy of 124.5 Mev with the Berkeley heavy-ion linear accelerator. The experimental equipment and techniques are discussed. The angular distributions show the same general behavior as previous heavy-ion elastic scattering experiments. The experimental data were analyzed with the semiclassical Blair model as modified by McIntyre. Very good agreement with experiment was obtained. The measurements were taken with 1% statistics in order to study the structure of the angular distributions in greater detail, because only by fitting the details in the structure was it possible to obtdin unambiguous sets of parameters. The parameters indicated a nuclear radius of 1.45A/sup 1/3/ x 10/sup -13/ cm, and a nearly constant surface thick ness of 1.6 x 10/sup -13/ cm. Total reaction cross sections were obtained. A rainbow-model analysis by Goldman of the data is given. Existing alpha - and heavy-ion scattering data were analyzed with the McIntyre model and compared with previous optical-model analyses of the same data. It was found that, by independent analysis, the two models give the same imaginary phase shifts for all partial …