210 ON THE PHYSICi^L STRUCTURE OF THE EARTH. 



of the Earth's density from its surface to its center is, moreover, a fact 

 clearly revealed by the mean density of the I'arlh l)eiii,n' double that of 

 the materials composin*;- the outside of its solid shell. 



If the increase of density iu going Irom the surface to the center of 

 a large mass of lliiid is due to compression exeicised by the outer upon 

 the inner strata, it follows that the greater the total quantity of tluid 

 the greater will be the dilfereuce between the density at its surface and 

 its center, and the less the cpiantity of fluid the less will be this differ- 

 ence. With a small spheroid of compressible fluid the variation of 

 density might be neglected and the mass regarded 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 ^ w, 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 center to surface. The outer surface will now present an 

 ellipticity less that !f 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 center 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 supi)0se 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 center. Let the outer strata of equal density be suc- 

 cessively removed, so as to leave a succession of free fluid surfaces, until 

 a spheroid is reached in which the diflerence of density is insensible. It 

 is manifest that with each successive removal of the u[)per stratum of 

 liquid the compression in the remaining strata becomes reduced, and 

 also the variation in density from surface to center, until this variation 

 becomes altogether extinguished. With the same velocity of rotation, 

 the ellipticities of the surfaces of liquid thus successively exposed would 

 increase up to the limiting value, f m. 



If at any time of the Earth's solidilication we suppose a nucleus of 

 fluid to be inclosed within the si»lid shell, the successive increasing of 

 thickness of the shell, from the congelation of the fluid matter of the 

 nucleus, must be accompanied by the removal of successive outer strata 

 from the nucleus. From what has been seen already, the nucleus will 

 tend to acquire an increase of ellipticity, and therefore to mould the 

 semifluid ])asty matter about to pass into a solid state into a shape dif- 

 ferent from what it would have if no change whatever in the position of 

 the particles had taken ])lace. As tiie nucleus is supposed to be in a 

 state of fusion from heat, the successive additions to the inner surface 

 of the shell from the matter of the nucleus must jiroceed at a very slow 

 rate. The congelation of the surface stratum of tUe nucleus nmst be a 

 process of (he same onler of slowness as the flow of heat through the 

 shell; and the matheniatical theory of conduction established by Fourier 



