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A precision measurement of the spin structure function g{sub 1}(x,Q{sup 2}) for both the proton and deuteron was made using deep inelastic scattering of the 48.35 GeV polarized electron beam at the Stanford Linear Accelerator Center. The kinematic range of the measurement was 0.014 &lt; x &lt; 0.9 and 1 (GeV/c){sup 2} &lt; Q{sup 2} &lt; 40 (GeV/c){sup 2}. Solid {sup 15}NH{sub 3} and {sup 6}Li{sup 2}H were used as target materials. The beam polarization of 0.81 {+-} 0.02 was measured using Moeller polarimetry. The scattered electron events were accumulated in three magnetic spectrometers at fixed angles of 2.75{sup o}, 5.5{sup o}, and 10.5{sup o}. Data were obtained with the target polarization direction both parallel and transverse to the beam direction. Together with existing world data, the g{sub 1}(x,Q{sup 2}) results were fit in a well-established next-to-leading order QCD formalism, and are consistent with the Bjorken sum rule

A Precision Measurement of the Spin Structure Function g{sub 1}(x,Q{sup 2}) for the Proton and Deuteron