  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.
