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 darwinmodernscie00camb Year: 1909 552 The Genesis of Double Stars At length when the longest axis of the three has become about three times as long as the shortest1, the stability of this family of figures vanishes, and we have reached a new form of bifurcation and must look for a new type of figure along which the stable development will presumably extend
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 darwinmodernscie00camb Year: 1909 552 The Genesis of Double Stars At length when the longest axis of the three has become about three times as long as the shortest1, the stability of this family of figures vanishes, and we have reached a new form of bifurcation and must look for a new type of figure along which the stable development will presumably extend. Two sections of this critical Jacobian figure, which is a figure of bifurcation, are shown by the dotted lines in Fig. 3; the upper figure is the equatorial section at right angles to the axis of rotation, the lower figure is a section through the axis. Now Poincare' has proved that the new type of figure is to be derived from the figure of bifurcation by causing one of the ends to be prolonged into a snout and by bluntening the other end. The The 'pear-shaped figure' and the Jacobian figure from which it is derived. snout forms a sort of stalk, and between the stalk and the axis of rotation the surface is somewhat flattened. These are the character- istics of a pear, and the figure has therefore been called the ' pear- shaped figure of equilibrium.' The firm line in Fig. 3 shows this new type of figure, whilst, as already explained, the dotted line shows the form of bifurcation from which it is derived. The specific mark of this new family is the protrusion of the stalk together with the other corresponding smaller differences. If we denote this difference by c, while A + b denotes the Jacobian figure of bifurcation from which it is derived, the new family may be called A+b + c, and c is zero initially. According to my calculations this series of figures is stable2, 1 The three axes of the ellipsoid are then proportional to 1000, 432, 343. M. Liapounoff contends that for
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