40 



Configurations of Equilibrium [CH. m 



regard the series of Jacobian ellipsoids as starting at the value a = b (the 

 point of bifurcation), and the ratio a/6 continually increases from 1 to oc as 

 we pass along the series. The following numerical values are given by 

 Darwin*. 



40. We have found that there are two linear series of ellipsoidal con- 

 figurations the Maclaurin spheroids and the Jacobian ellipsoids. The 

 stability of these figures can now be investigated by the methods already 

 explained. 



Stability when angular velocity is increased, as in 

 Plateau's experiments 



41. 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 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. 

 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 disc round which it clustered. As the speed of rotation increased the 

 globule 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 contemplated in the nebular hypothesis, for 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 velocity mechanically increased by the medium of the wire and disc. 



* Coll. Works, in. p. 130. 



