  We report a comprehensive polarized and unpolarized neutron scattering study
of the evolution of the dynamical spin susceptibility with temperature and
doping in three underdoped single crystals of the \YBCO{6+x} high temperature
superconductor: \YBCO{6.5} (Tc = 52 K), \YBCO{6.7} (Tc = 67 K), and \YBCO{6.85}
(T_c = 87 K). Theoretical implications of these data are discussed, and a
critique of recent attempts to relate the spin excitations to the
thermodynamics of high temperature superconductors is given.
