Archive image from page 585 of Darwin and modern science; essays. Darwin and modern science; essays in commemoration of the centenary of the birth of Charles Darwin and of the fiftieth anniversary of the publication of the Origin of species darwinmodernscie00sewa_0 Year: 1909 The planetary figure becomes unstable 551 According to Poincare's principle the vanishing of the stability serves us with notice that we have reached a figure of bifurcation, and it becomes necessary to inquire what is the nature of the specific difierence of the new family of figures which must be coalescent with the ol
Archive image from page 585 of Darwin and modern science; essays. Darwin and modern science; essays in commemoration of the centenary of the birth of Charles Darwin and of the fiftieth anniversary of the publication of the Origin of species darwinmodernscie00sewa_0 Year: 1909 The planetary figure becomes unstable 551 According to Poincare's principle the vanishing of the stability serves us with notice that we have reached a figure of bifurcation, and it becomes necessary to inquire what is the nature of the specific difierence of the new family of figures which must be coalescent with the old one at this stage. This difierence is found to reside in the fact that the equator, which in the planetary family has hitherto been circular in section, tends to become elliptic. Hitherto the rotational momentum has been kept up to its constant value partly by greater speed of rotation and partly by a symmetrical bulging of the equator. But now while the speed of rotation still increases, the equator tends to bulge outwards at two diametrically opposite points and to be flattened midway between these protuberances. The specific diffierence in the new family, denoted in the general Fig. 2. Planetary spheroid just becoming unstable. sketch by h, is this ellipticity of the equator. If we had traced the planetary figures with circular equators beyond this stage we should have found them to have become unstable, and the stability has been shunted off' along the A-\-h family of forms with elliptic equators. This new series of figures, generally named after the great mathematician Jacobi, is at first only just stable, but as the density increases the stability increases, reaches a maximum and then de- clines. As this goes on the equator of these Jacobian figures becomes more and more elliptic, so that the shape is considerably elongated in a direction at right angles to the axis of rotation. 1 The mathematician familiar with Jacobi's ellipsoid will find that this is correct, alth
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