Spin asymmetries<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and structure functions<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>of the proton and the deuteron from polarized high energy muon scattering

We present the final results of the spin asymmetries ${A}_{1}$ and the spin structure functions ${g}_{1}$ of the proton and the deuteron in the kinematic range $0.0008&lt;x&lt;0.7$ and $0.2&lt;{Q}^{2}&lt;100{\mathrm{GeV}}^{2}.$ For the determination of ${A}_{1},$ in addition to the usual method which employs inclusive scattering events and includes a large radiative background at low x, we use a new method which minimizes the radiative background by selecting events with at least one hadron as well as a muon in the final state. We find that this hadron method gives smaller errors for $x&lt;0.02,$ so it is combined with the usual method to provide the optimal set of results.