Preface; 1. On the influence of geological changes on the Earth's axis of rotation; 2. On Professor Haughton's estimate of geological time; 3. On a suggested explanation of the obliquity of planets to their orbits; 4. Note on the ellipticity of the Earth's strata; 5. On an oversight in the Méchanique Céleste, and on the internal densities of the planets; 6. On the figure of equilibrium of a planet of heterogeneous density; 7. The theory of the figure of the Earth carried to the second order of small quantities; 8. On Jacobi's figure of equilibrium for a rotating mass of fluid; 9. On figures of equilibrium of rotating masses of fluid; 10. Ellipsoidal harmonic analysis; 11. On the pear-shaped figure of equilibrium of a rotating mass of liquid; 12. The stability of the pear-shaped figure of equilibrium of a rotating mass of liquid; 13. On the integrals of the squares of ellipsoidal surface harmonic functions; 14. The approximate determination of the form of Maclaurin's spheroid; On the figure and stability of a liquid satellite; Index.