On Riemann's Criterion for the Stability of Liquid Ellipsoids

The energy criterion used by Riemann to discuss the stability of the ellipsoids that now hear his name is shown to be incorrect except under special circumstances. These circumstances prevail in the problem of the stability of the Maclaurin spheroids, where Riemaun's well-known criterion for the onset of instability has been amply verified. The incorrectness of the criterion in general explains the discrepancies between Riemann's stability results on the one hand, and Chandrasekhar's on the other.