Physical Structure of the Earth. 243 



(5) Before presenting my conclusions on the shape of the 

 inner surface of the solidified shell and Plana's remark relative 

 to the same subject, it is necessary to recall some results esta- 

 blished by Clairaut, and frequently put forward by mathema- 

 tical investigators of the Earth's figure. It seems to be uni- 

 versally admitted that if a mass of heterogeneous fluid com- 

 posed of strata of equal density, each increasing in density 

 from the surface of the mass to its centre, is set in rotation, 

 the several strata will be spheroidal, but their ellipticities will 

 not be equal. The ellipticities will decrease from the outer 

 surface towards the centre. This law of decrease of ellip- 

 ticity towards the centre is not a hypothetical result, but a 

 necessary deduction from the properties of fluids. As all 

 known fluids are compressible, such an arrangement of strata 

 of equal density as that referred to must follow from the 

 supposition of the existence of any mass of fluid of such 

 magnitude as the whole Earth. The increase of the Earth's 

 density from its surface to* its centre is, moreover, a fact 

 clearly revealed by the mean density of the Earth being 

 double that of the materials composing the outside of its solid 

 shell. 



If the increase of density, in going from the surface to the 

 centre of a large mass of fluid, is due to compression exer- 

 cised by the outer upon the inner strata, it follows that the 

 greater the total quantity of fluid the greater will be the 

 difference between the density at its surface and its centre, 

 and the less the quantity of fluid the less will be this dif- 

 ference. With a small spheroid of compressible fluid, the 

 variation of density might be neglected, and the mass re- 

 garded as homogeneous. Suppose such a small mass of fluid 

 to be set in rotation, its surface will become spheroidal, and 

 it will have the well-known ellipticity f m, where m is 

 the ratio of centrifugal force to gravity at the equator of the 

 spheroid. If, now, this original spheroid be supposed to be 

 overlaid with masses of the fluid, one after another, the inner 

 portions will be sensibly compressed, and the whole mass will 

 begin to vary in density in going from centre to surface. The 

 outer surface will now present an ellipticity less than J m. 

 If fresh layers of fluid are continually applied to the outer 

 surface, the variation of density will continue, and the differ- 

 ence between the density at the centre and surface will increase. 

 The ellipticity of the outer stratum of fluid will at the same 

 time diminish to a value corresponding to the law of density. 

 Let us now reverse this operation, and suppose a great mass 

 of liquid in rotation, its outer stratum will be less dense than 

 those beneath, and its greatest density must be at the centre. 



