III. On Jacobi's theorem respecting the relative equilibrium of a revolving ellipsoid of fluid; and on Ivory's discussion of the theorem

Jacobi discovered the theorem that a fluid ellipsoid revolving with uniform angular velocity round its least axis might be in equilibrium. Ivory discussed the theorem, and made several statements regarding the limitations of the proportions of the axis. Ivory’s statements contain various errors and truths based on erroneous reasoning. The object of the present memoir is to correct Ivory’s errors, to supply his imperfections, and to add something to what is already known respecting the theorem.