PHYSICAL ASTRONOMY. 299 



302. A homogeneous fluid, therefore, of the 

 same mean density with the Earth, and revol- 

 ving on an axis in the space of %3 h 56 m 4 sec of 

 solar time, would be in equilibria if it had the 

 figure of an oblate spheroid, of which the axis 

 was to the equatorial diameter as 230 to 



This is accordingly the figure which NEWTON a- 

 scribes to the Earth. Princip. lib. 3. prop. 19. 



In the spheroid thus constituted, the gravitation at 

 the equator will be to that at the pole as 229 to 

 230 ; and if g be the gravitation at the equator, 

 and g f that at any other point, of which the lati- 



tude is A, g' = g ( 1 + ^ 5 also if I be the 



length of the pendulum that vibrates seconds at the 

 equator, and V the length of a pendulum that does 



the same in Latitude A, /' = I ( 1 -J -? ^ \ 



NEWTON'S investigation of the figure of the Earth, 

 though very ingenious, involved some assumptions 

 which prevented it from being quite satisfactory. 

 A very accurate and elegant demonstration was af- 

 terwards given by MACLAURIN ; and the investiga- 

 tion was improved and rendered more analytical 

 by CLAIRAUT, Fig. de la Terre. 



But 



