Measurement of σ _total in e⁺e^- annihilations below 10.56 GeV

Using the CLEO III detector, we measure absolute cross sections for e⁺e^- → hadrons at seven center-of-mass energies between 6.964 and 10.538 GeV. R, the ratio of hadronic and muon pair production cross sections, is measured at these energies with a r.m.s. error <2% allowing determinations of the strong coupling α _s. Using the expected evolution of α _s with energy we find α _s (M_Z² 0.126 ± _-0.011^+0.015, and Λ 0.31 _-0.08-0.21^+0.09+0.29.