I. On the instability of the pear-shaped figure of equilibrium of a rotating mass of liquid

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Abstract
1. The main result obtained in this paper is sufficiently indicated by its title. In a recent paper I showed that the stability of the pear-shaped figure could only be decided on after the figure itself had been calculated as far as terms involving the cube of the parameter e , which is used to measure the deviation of the pear-shaped figure from the critical Jacobian ellipsoid. In the present paper these third-order terms are calculated, and the pear-shaped figure is definitely shown to be unstable. A statement of the results obtained, and a discussion of their bearing on the wider question of which this problem forms a part, will he found at the end of the paper (§§ 23-27).

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