EAR 



Let p and p' be the lengths of two pendulums oscillating seconds in la- 

 titudes A and A', c tlie compression, the equatorial radium being unity j. 

 then 



c _ pp' 



jtsin. A p'sin.2 A' 



5. Comparison of the figure of the earth, deduced from actual admea- 

 surement of a degree in different latitudes, with that deduced from the 

 theory of gravity. 



If a homogeneous fluid revolve on an axis, it will form itself into an 

 oblate spheroid, of which the Polar | axis : radius of Equator : : attrac- 

 tion at Equator centrifugal force at Equator : attraction at tlie Pole. 



In the case of the earth, this ratio will be :: 229 : 230. 



If the earth be not homogeneous, but composed of strata that increase 

 in density towards the centre, the spheroid will have less oblateness than 

 if it were homogeneous, and it is demonstrable that if the density in- 

 crease so that it be infinite at the centre, the ellipticity -r=o which is 



oTo 



the case of the least ellipticity ; -^ is the case with the greatest. 

 Hence as the ellipticity of the earth has been shewn to be less than 



230" ^ viz ' "312") ' Jt is eviaent tnat if tne eartn is a spheroid of equili- 

 brium, it is denser towards the interior. This has been indisputably 

 proved to be the case by actual experiment. See Mountain, attraction of. 



But after all, whether the eatth be a spheroid of equilibrium, whether 

 the N. and S. f spheres be equal and similar to each other, and whn.t is 

 the ratio of an arc of the meridian, measured ia a given latitude, to tna 

 whole meridian, are questions to which complete solutions have not yet 

 been given. 



