Abstract
Employing second order virial equations and super-potential, we investigate stability to the second-harmonic of the spheroidal homogeneous liquid figures reported in I, whose equilibrium is due to an internal motion of differential rotation. The angular velocity, which for equilibrium it was enough to be specified on the body's boundary surface, is now required throughout its interior, two alternatives being physically acceptable: constant over cylinder surfaces; or constant over disks; these two distributions are subjected to Goldreich's criterium for local stability. Just as in Maclaurin's sequence, a figure of neutral frequency and a region of instability are found in each of our series.
