DOUBLE STARS 153 



case, now becomes increasingly greater. For a time the 

 condition of the ellipsoidal form of the liquid mass is 

 stable, and all continues well, but at length it reaches a 

 second crisis in its career, beyond which, if it were to 

 continue as an ellipsoid, it would become unstable and 

 would meet with inevitable destruction. The section 

 through its polar axis and its greatest equatorial diameter 

 is now represented in fig. 7. Denoting its polar axis by. 

 i, the greatest equatorial diameter is 2-9, and the least 

 equatorial diameter, drawn through the centre and at right 

 angles to the paper, is 1-25. Its period of rotation is now 

 1 1 times that of the spheroid in fig. 6. 



A third form of stable equilibrium which the rotating 

 fluid mass may assume after passing the limiting form of 

 stability of Jacobi's ellipsoid, has been recently discovered 

 by Poincare". It has somewhat the form of a pear. Upon 

 one side of the axis of rotation of Jacobi's ellipsoid, the 

 longer equatorial axis becomes shorter, and on this side the 

 figure becomes fatter, while upon the other side the long 

 equatorial diameter becomes still longer, and upon that 

 side the figure becomes thinner. There is, further, a 

 suggestion of constriction or waist round the figure not 

 far from its middle. M. Poincare's first attempt to trace 

 the form is shown in fig. 8, but Darwin has recently shown 

 that the resemblance to a pear is not so strongly marked 

 as Poincar6 had supposed. This point marks the limit to 

 which it has so far been possible to apply mathematical 

 methods to the problem, and the further development of 

 the pear-shaped figure is unknown. Although, however, 

 we can only proceed by speculation, it is impossible to 

 restrain the imagination in its attempt to trace the course 

 of development further. Darwin and Poincare are both 

 of opinion that the resemblance to a pear would become 

 more pronounced by the further development of the waist, 



