  We have measured the proton and deuteron spin structure functions g_1^p and
g_1^d in the region of the nucleon resonances for W^2 < 5 GeV^2 and $Q^2\simeq
0.5$ and $Q^2\simeq 1.2$ GeV^2 by inelastically scattering 9.7 GeV polarized
electrons off polarized $^{15}NH_3$ and $^{15}ND_3$ targets. We observe
significant structure in g_1^p in the resonance region. We have used the
present results, together with the deep-inelastic data at higher W^2, to
extract $\Gamma(Q^2)\equiv\int_0^1 g_1(x,Q^2) dx$. This is the first
information on the low-Q^2 evolution of Gamma toward the Gerasimov-Drell-Hearn
limit at Q^2 = 0.
