in the interior Parts of the Earth. 3'i3 



and France. It is thus proved, tliat when observations are 

 made at stations sufficiently distant from one another, and are 

 judiciously combined in calculation, the effects of local and 

 accidental discrepancies disappear, and a mean result is ob- 

 tained demonstrating that the earth is possessed of a figure 

 much more regular than all former inquiries led to expect. 

 The two ellipticities, -^^-^ and ^^g, are to one another as 15 to 

 16. It may be impossible to fix with any degree of precision 

 the degree of approximation that may reasonably be expected 

 in this investigation ; but it is sufficiently honourable for mo- 

 dern science to have ascertained within such narrow limits a 

 quantity which is known to us only by effects extremely mi- 

 nute and complicated, whether we regard the differences of 

 the degrees of the meridian, or the variation of the length of 

 the pendulum, or the small inequalities of the moon's motion. 



It is remarkable that the ellipticity deduced from Captain 

 Sabine's experiments is exactly equal to the proportion of the 

 centrifugal force to gravity at the equator. Supposing the 

 earth to have been originally fluid, the ellipticities of the strata 

 varying in density from the centre to the surface, would be 

 caused bv the centrifugal force. If the rotatory motion of the 

 earth, supposing it fluid, were stopped, the ellipticities would 

 disappear, and the figure would change to a perfect sphere. 

 Again, if there were no variation of density from the centre to 

 the surface, the ellipticities of the several strata would likewise 

 be constantly the same. Thus the ellipticities, although caused 

 by the centrifugal force, are yet modified by the densities. If 

 the law of the ellipticities were known, we should likewise 

 know the law of the densities, and the degree of pressure that 

 prevails at any distance from the centre. But in reality our 

 knowledge is confined to the ellipticity at the surface, and to 

 the proportion it bears to the centrifugal force, which is not 

 sufficient to enable us to investigate the density and pressure 

 in the interior parts. 



It follows from the relation which is found by observation 

 to subsist between the ellipticity at the surface and the centri- 

 fugal force, on the one hand, that the earth, supposing it ori- 

 ginally fluid, could not have been homogeneous, or of the 

 same density from the centre to the surface ; and, on the other, 

 that the gravitation could not be directed to one point, or 

 centre. For, on one supposition, the ellipticity must be ex- 

 actly I of the centrifugal force, and, on the other, \ of it. All 

 the experiments concur in proving that the actual ellipticity 

 is considerably removed from either extreme case, although it 

 falls between them ; and hence we must conclude that the 

 earth, in a fluid state, could only consist of strata varying in 

 S s 2 density 



