584 EQUILIBRIUM OF ROTATING MASSES OF LIQUID. [CHAP. XII 



The fastest rotation which admits of an ellipsoidal form of revolution, 

 for such a mass, has a period of 2 h. 25 m. 



If m be the total mass, h its angular momentum, we have 



whence we find 



f 



m 



This gives the angular momentum of a given volume of given 

 fluid in terms of f, and thence in terms of the excentricity e. 

 It appears from the discussion of an equivalent formula by 

 Laplace, or from the table given below, that the right-hand 

 side increases continually as f decreases from oo to 0. Hence 

 for a given volume of given fluid there is one, and only one, 

 form of Maclaurin s ellipsoid having any prescribed angular mo 

 mentum. 



The following table, giving numerical details of a series of Maclaurin s 

 ellipsoids, is derived from Thomson and Tait*, with some modifications intro 

 duced for the purpose of a more ready comparison with the corresponding 

 results for Jacobi s ellipsoids, obtained by Darwin (see Art. 315). The unit of 

 angular momentum is m^ a^. 



* Natural Philosophy, Art. 772. 



