  We test the Gerasimov-Drell-Hearn (GDH) sum rule numerically by calculating
the total photon absorption cross sections $\sigma_{1/2}$ and $\sigma_{3/2}$ on
the nucleon via photon excitation of baryon resonances in the constituent quark
model. A total of seventeen, low-lying, non-strange baryon resonances are
included in this calculation. The transverse and longitudinal interference
cross section, $\sigma_{1/2}^{TL}$, is found to play an important role in the
study of the $Q^2$ variation of the sum rule. The results show that the GDH sum
rule is saturated by these resonances at a confidence level of 94%. In
particular, the $P_{33}(1232)$ excitation largely saturates the sum rule at
$Q^2 = 0$, and dominates at small $Q^2$. The GDH integral has a strong
$Q^2$-dependence below $Q^2= 1.0 {GeV}^2$ and changes its sign around $Q^2= 0.3
{GeV}^2$. It becomes weakly $Q^2$-dependent for $Q^2 > 1.0 {GeV}^2$ because of
the quick decline of the resonance contributions. We point out that the $Q^2$
variation of the GDH sum rule is very important for understanding the nucleon
spin structure in the non-perturbative QCD region.
