246 Prof. H. Henness3 r on the 



shell would have a smaller ellipticity than its outer surface, 

 and the strata of the shell, as well as those of the nucleus, would 

 be less oblate in going from the outer surface. 



(6) It is important to distinctly bear in mind that the con- 

 stitution of the shell and nucleus indicated by the foregoing 

 reasonings is not based on any hypothesis of a specific law of 

 density of the interior strata of the Earth. It is a deduction 

 from the established properties of fluids quite as rigorous 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 

 ellipticity 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 fundamental 

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

 of the thickness of the shell. But when the fundamental 

 assumption on which this ratio is calculated is shown to be in 

 contradiction to physical and mechanical laws, the whole of 

 the conclusions drawn from such a calculation must fall to the 

 ground. 



In the Mdcanique Celeste, Laplace, following Clairaut, 

 proved that if the density in a fluid spheroid decreases from 

 the centre to the surface, the ellipticity of the strata of equal 

 density must decrease from the surface towards the centre. 

 This result forms the groundwork of some of the arguments 

 employed in the present inquiry. Legendre and Laplace also 

 deduced a law of density from the properties of compressible 

 fluids, and from this law the latter unfolded a law of ellip- 

 ticity of the strata of equal density. The results arrived at in 

 my present inquiry are manifestly totally independent of the 



law of density p = — , deduced by Legendre and Laplace. 



In order to apply this law to the strata of the solidified shell, 

 the assumption must necessarily be made that the particles of 

 the fluid underwent no change in position on passing to the 

 solid state. This was assumed by Mr. Hopkins and Arch- 

 deacon Pratt; and, as we have seen, such an assumption 

 is not only unwarranted, but is absolutely contradicted by the 

 established laws of hydrodynamics. My conclusions are not 

 only in harmony with those laws, but necessarily require them 

 to be kept constantly in view throughout the whole investi- 

 gation. 



