ABSTRACT
Investigations of spinning fluid masses go back to the time of Newton who, assuming the asphericity to be small, determined the flattening of the Earth by modelling it as such. Later, Maclaurin determined the equilibrium shapes of oblate fluid rotators, the so-called Maclaurin ellipsoids. He further showed that prolate equilibrium shapes cannot be obtained. Truly triaxial ellipsoidal shapes of equilibrium for spinning fluids were not supposed to be realisable until Jacobi put forth an argument in support of their existence. These ellipsoids branch off from the Maclaurin sequence and are called the Jacobi ellipsoids. The equilibrium shapes of spinning fluid ellipsoids are comprehensively covered by Chandrasekhar (1969) in a unified manner, using the volume-averaged method introduced below.
