152 



THE EVOLUTION OF 



a needle balanced upon its point on a plate of glass, they 

 would, upon the slightest disturbance, instead of tending 

 to revert to their original condition, tend to diverge still 

 further from it, and, this action continuing, the whole mass 

 would rapidly break up in some unpredictable manner, 

 unless it happened to fall into some other form that was 

 stable. Outside mathematical analysis permanent unstable 

 forms of equilibrium are impossible. 



On passing this first critical stage in its history, the 

 mass of rotating liquid ceases to be a spheroid. It acquires 



Axis of rotation. 



FIG. 7. Critical form of Jacobi's ellipsoid. 



a figure in which the equatorial section is no longer a 

 circle. This section becomes, like the one through the polar 

 axis, an ellipse. The figure is now known as an ellipsoid, 

 and it was found to be a figure of equilibrium of a rotat- 

 ing liquid mass by Jacobi about the year 1850. Upon 

 continued application of the twist the ellipsoidal form 

 becomes more and more developed, the polar axis becom- 

 ing shorter, the greater equatorial diameter increasing 

 still further, and the one at right angles to it becoming 

 less. The remarkable fact, however, appears, that with 

 continued application of twist the period of rotation, 

 instead of becoming shorter, as had previously been the 



