Doping Dependence of the Magnetic Resonance Peak in YBa_2 Cu_3 O_{6+x}

We report inelastic neutron scattering experiments on the doping dependence of the energy and spectral weight of the sharp magnetic resonance peak in YBa_2 Cu_3 O_{6+x}. These measurements also shed light on the relationship between the magnetic excitations in the normal and superconducting states.