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Critical current measurements were made on the Pb-Bi system for bismuth concentrations between 1 atomic % and 15 atomic %. Specimens were prepared by evaporation techniques and.were of rectangular geometry with thicknesses of the order of 10,000 Å. Measurements were mainly confined to the surface sheath state with applied fields ranging from Hc2 to Hc3. Critical currents in fields applied perpendicular and parallel to specimen surfaces yielded the variation of Hc2 (4.2∞K) and Hc3 (4.2°K) with alloy composition. In parallel fields close to Hc3, the critical current was proportional to specimen width for changes in width from 0.5 mm to 5.0 mm. Critical currents were also measured with the applied field inclined at an angle φ to the surfade.