V 



PHYSICAL ASTRONOMY. 301 



ways be two elliptic spheroids, and not more, 

 in which an equilibrium may be maintained. 



If the density of the fluid is greater than the mean 

 density of the Earth, the time of rotation with 

 which the equilibrium ceases to be possible, is 

 had, by dividing 2h 25 m I7 se c by the square root 

 pf the density of the fluid, that of the Earth being 

 unity. LA PLACE, Theorie du Mouvement et dc 

 la Figure des Planetes, Paris, 1784-, p. J26. 



304. If the fluid mass, supposed to revolve on 

 its axis, be not homogeneous, but be composed 

 of strata that increase in density toward the 

 centre ; the solid of equilibrium will still be an 

 elliptic spheroid, but of less oblateness than if 

 it were homogeneous. 



This was demonstrated by CLAIRAUT, Theorie> &c. 

 NEWTON fell into the mistake of supposing the 

 contrary to be the case, or that the greater densi- 

 ty toward the centre would be accompanied with 

 greater oblateness. If the density increase, so as 

 at the centre to be infinite, the ellipticity is 



2 x 289 = ~57lf wn i cn is the case of the least el- 

 lipticity. - is the case of the greatest. 



305. Hence 



