  We study epicyclic oscillations of fluid tori around black holes (in the
Paczynski-Wiita potential) and derive exact analytic expressions for their
radial and vertical eigenfrequencies nu_r and nu_z to second-order accuracy in
the width of the torus. We prove that pressure effects make the
eigenfrequencies smaller than those for free particles. However, the particular
ratio nu_z/nu_r=3/2, which is important for the theory of high-frequency
quasi-periodic oscillations (QPOs), occurs when the fluid tori epicyclic
frequencies nu_r and nu_z are about 15% higher than the ones corresponding to
free particles. Our results therefore suggest that previous estimates of black
hole spins from QPOs have produced values that are too high.
