  A comprehensive inelastic neutron scattering study of magnetic excitations in
the near-optimally doped high-temperature superconductor ${\rm
YBa_{2}Cu_{3}O_{6.85}}$ is presented. The spin correlations in the normal state
are commensurate with the crystal lattice, and the intensity is peaked around
the wave vector characterizing the antiferromagnetic state of the insulating
precursor ${\rm YBa_{2}Cu_{3}O_{6}}$. Profound modifications of the spin
excitation spectrum appear abruptly below the superconducting transition
temperature, $\rm T_C$, where a commensurate resonant mode and a set of weaker
incommensurate peaks develop. The data are consistent with models based on an
underlying two-dimensional Fermi surface that predict a continuous, downward
dispersion relation connecting the resonant mode and the incommensurate
excitations. The magnetic incommensurability in the ${\rm
YBa_{2}Cu_{3}O_{6+x}}$ system is thus not simply related to that of another
high temperature superconductor, ${\rm La_{2-x}Sr_xCuO_{4}}$, where
incommensurate peaks persist well above $\rm T_C$. The temperature dependent
incommensurability is difficult to reconcile with interpretations based on
charge stripe formation in ${\rm YBa_{2}Cu_{3}O_{6+x}}$ near optimum doping.
