144 THE TIDAL PROBLEM. 



The points of bifurcation and conditions of stability or instability depend 

 only upon the shape of the figures, while the shapes of the figures in the va- 



0? 



rious series depend only upon the values of ^^-^^^ . Consequently if a rotat- 

 ing homogeneous fluid body contracts in such a way as to remain always 

 homogeneous, its shape and condition as to stability are determined by this 

 function throughout the whole series of changes. 



