Absolute pp-elastic-differential cross sections were measured at incident energies 492, 576, 642, 728, and 793 MeV from about 30' to 90' c.m. The total uncertainty was determined to be less than 170, made possible by particle counting for beaxn normalization and extensive cross-checks of systematic eQects. These new data are consistent with previous data above 600 MeV but have uncertainties about a factor of 10 smaller. Near 500 MeV these data are consistent with 90' data from TRIUMF, but differ signi6cantly from similar data from PSI; the cause of this discrepancy is discussed.PACS number(s): 25.40.Cm, 25.10.+s 'Present address: