Q^2-Dependence of the Proton's G_1 Structure Function Sum Rule

We study the $Q^2$ variation of the first moment of the nucleon's spin-dependent structure function $G_1$. As $Q^2 \rightarrow 0$ the moment is determined by the low energy theorem for Compton scattering. In the deep-inelastic region the moment is calculated using twist expansion to order $1/Q^2$. Based on these limits, we construct a formula which smoothly interpolates between the two regions.