212 



ON THE PHYSICAL STRUCTURE OF THE EAKTll. 



center. This arrangement is necessarily followed by a mass of Ihiid 

 under such conditions as the nucleus, or under the conditions of the 

 entirely lluid Earth. If the matter com- 

 posing the Earth underwent no change 

 in ijassing from the tluid to the solid 

 state, instead of the arrangement here 

 represented, the inner surface of the 

 shell would have a smaller ellipticity 

 than its outer surtju^e, and the strata 

 of the shell, as well as those of the nu- 

 cleus, would be less oblate in going 

 from the outer surface. 



(<!) It is important to distinctly bear 

 in mind that the constitution of the 



shell and nucleus indicated by the foregoing reasonings Is not based 

 on any hypothesis of a specilic law of density of the interior strata 

 of the Earth. It is a deduction from the established properties of 

 fluids (juite as vigorous as the conclusions regarding the spheroidal 

 shape of a mass of rotating liquid. On the other hand, the supposition 

 tacitly or openly made by Mr. Hopkins and his followers, that the ellip- 

 ticity of the inner stratum of the solid shell is precisely the same as that 

 which this stratum had when fluid, is not merely a hypothesis — it is an 

 assumption which is directly contradicted by the recognized physical 

 properties of all known liquids, and even contradicted by the funda- 

 mental principles of hydrodynamics. Upon this assumption was based 

 the calculation of the ratios of the inner and outer ellipticities of the 

 shell which would correspond to the observed value of the i)recession 

 of the Earth's axis, and hence the limiting value of the thickness of the 

 shell. But when the fundamental assumption ou which this ratio is 

 calculated is shown to be in contradiction to i^hysical and mechanical 

 laws, the whole of the conclusions drawn from such a calculation must 

 fall to the ground. 



In the Mecanique Celeste, Laplace, following Olairaut, proved that if the 

 density in a fluid spheroid decreases from the center to the surface, the 

 ellipticity of the strata of equal density must decrease from the surface 

 towards the center. This result forms the groundwork of some of 

 the arguments employed in the present impiiry. Legendre and La- 

 place also deduced a law of density from the properties of compres- 

 sible fluids, and from this law the latter unfolded a law of ellipticity 

 of the strata of equal density. The results arrived at in my pres- 

 ent in(iuiry are manifestly totally independent of the law of density 



p = '"-^ , deduced by Legendn*, and Laplace. In order to 



a|»i>ly this law to the strata of the solidified shell, the assumption 

 must necessarily be made that the particles of the tliiul underwent 

 no change in position on i)assing to the solid state. This was assumed 



