tation has been diminished to a certain extent, the stability is found to cease, and Mr. Jeans determines the new series of cylinders coalescent with the elliptical cylinder to be pear-shaped in section. He was also able to prove with comparative ease that the cylinders of pear-shaped section are stable. It was here that he began to reap the advantage of the comparative simplicity of conditions, for he was able to follow the deformation of the pear-shaped section until it became strongly marked, and he showed that the stability is maintained throughout.
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Fig. 4—Diagram illustrative of the Sequence of Ideas
The Figures 5 show the sections traced by Mr. Jeans of the cylinders; the lower of the two corresponds to a more advanced stage of development, and is drawn with slightly less accuracy than the upper one. It was not found possible to pursue the changes to a yet further stage, but the analysis clearly pointed to the separation of a satellite cylinder revolving round the parent or planetary cylinder. The mass of the satellite is as yet undetermined, but it is certainly somewhat small relatively to its parent.
The perfect analogy which subsists between this very ideal problem and the more realistic one considered previously is such as to justify us in feeling practically certain that our conjecture as to the development of the pear-shaped figure of Poincaré is correct.
These results, then, clearly indicate the tendency of a fluid planet to divide into two parts of unequal sizes. This result is brought about by a gradual change in the rotation, the rate of spinning augmenting up to a certain stage and then diminishing. This conclusion is wholly independent of the scale on which the figure is drawn and of the density of the fluid.
With the view of applying these ideas to the origin of satellites we have to consider what physical cause there may be which could produce a gradual change in the rate of spinning in the way postulated. The answer is that the cooling of a heated mass of liquid would have this effect—just as in Laplace's theory the contraction through cooling would cause an acceleration of the rate of spinning when the body has the orange shape of a planet. When we reach the ellipsoidal figures, however, we have to postulate that contraction shall have exactly the opposite effect and make the body spin slower. This sounds at first like blowing hot and cold, and it will naturally raise a doubt as to the possibility of the effect. But it may be asserted that the argument does remain correct, for the amount of rotation in a body is made up of two factors, namely, the rate of its spinning and another factor depending on the distribution of the mass with reference to
