ELLIPSOIDAL FIGURES OP EQUILIBRIUM. 



141 



The equations associated with db state that the figure is an eUipsoid, and 

 relate the eccentricity given by the point of this curve with the eccentricity 

 of the other principal section by means of elliptic integrals.* From this point 

 of view the figures corresponding to points on the curve bd are quite dis- 

 tinct from those on be, and it is regarded simply as an interesting fact that 

 they are the same in shape and differ only by their orientation in space. For 

 sufficiently small w there are two figures of this kind. When (o increases 



= 0.18709 . . . they become identical with each other and 



so that 



w 



27:/cV 



with the Maclaurin spheroid and vanish at this point. 



Figure 18 is a scale drawing of an axial section of the Maclaurin spheroid 

 corresponding to the point b of figure 17, and is therefore the figure from 

 which the Jacobian ellipsoids branch. The eccentricity of its axial section 

 is 0.813, or more than twice that of Saturn. In fact, there is no known 

 celestial mass condensed beyond the nebulous state which approaches the 

 oblateness of this theoretical figure of equilibrium. 



' Tisserand, M^canique Celeste, 2, Chap. VII. 



