Measurements of the Proton and Deuteron Spin Structure Function<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">g</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and Asymmetry<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">A</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

We have measured proton and deuteron virtual photon-nucleon asymmetries ${A}_{2}^{p}$ and ${A}_{2}^{d}$ and structure functions ${g}_{2}^{p}$ and ${g}_{2}^{d}$ over the range $0.03&lt;x&lt;0.8$ and $1.3&lt;{Q}^{2}&lt;10(\mathrm{GeV}/c{)}^{2}$ by inelastically scattering polarized electrons off polarized ammonia targets. Results for ${A}_{2}$ are significantly smaller than the positivity limit $\sqrt{R}$ for both targets. Within experimental precision the ${g}_{2}$ data are well described by the twist-2 contribution, ${g}_{2}^{\mathrm{WW}}$. Twist-3 matrix elements have been extracted and are compared to theoretical predictions.