212 The Configurations of Rotating Liquid Masses [ch. viii 
Stability when angular velocity is increasing , as in Plateaus experiments. 
195. In 1842 Plateau devised an experiment in which he attempted to 
observe directly the sequence of configurations in a rotating mass of fluid, with 
A globule of this mixture was then set in rotation in the oil by spinning a 
wire through its centre, the globule being kept in position on the wire by a 
was observed to flatten itself more and more until finally a dimple formed at 
the centre, and the globule detached itself from the disc in the form of a 
perfect ring. The conditions of this experiment were very different from 
those which prevail in astronomical masses, since the globule was not held 
together by its own gravitational attractions, but by surface tensions, and 
was not made to shrink while moving freely in space, but had its angular 
As a problem suggested by Plateau’s experiments, let us examine what 
would be the sequence of configurations assumed by a mass of gravitating 
matter which had its angular velocity continually increased by some mechanical 
means such as the spinning at an ever increasing rate of a pole through its 
centre. 
The possible configurations of equilibrium are those already discussed; so 
long as the mass is constrained to remain ellipsoidal, they consist of Maclaurin 
spheroids and Jacobian ellipsoids. To examine the stability of these figures 
we draw a diagram in which the angular velocity w is the vertical co-ordinate 
as in fig. 24, using the values of a> provided by Tables XVI and XVII. 
The stability of the Maclaurin spheroids is seen to be terminated by the 
occurrence of a point of bifurcation when to^/iiryp — 0*18712, the branch series 
Stability. 
a view to testing whether they were at all similar to those assumed by 
Laplace as the basis of his nebular hypothesis. Plateau mixed water and 
alcohol until they were of just the right density to float freely in olive oil. 
disc round which it clustered. As the speed of rotation increased, the globule 
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Fig. 24. 
velocity mechanically increased by the medium of the wire and disc.