THE PRESSURE WITHIN THE EARTH 73 



in present earth. The pressures in the present earth and in the 

 heterogeneous spheroid if e=.^ are shown graphically by the 

 upper curves in Fig. 2. The greatest rate of change of pres- 

 sures is seen to be at a point about .65 of the distance from the 

 center to the surface. 



Whatever the law of increase of density within the spheroid, 

 provided only that the density continually increases as we 

 approach the center, we may easily derive the following theorem: 



The pressure at the center of a heterogeneous spheroid differs from 

 the pressure at the center of the same matter in the spherical form, by 

 a fractional amount which is less than two-thirds the cllipticity of the 

 spheroid. 



Thus if the ellipticity is .06, the pressure at the center will 

 be not to exceed 4 per cent, less than if the matter was in the 

 spherical form. This shows that the changes in pressure due 

 to the changing ellipticity of the earth are limited in amount, 

 although important, and of the same order of magnitude as the 

 ellipticity. 



Another roughly approximate method of estimating the 

 pressures within the heterogeneous spheroid consists in assum- 

 ing that all the strata of equal density have the same ellipticity 

 as the surface. As a matter of fact, the ellipticity of the strata 

 decrease as we approach the center by a law which may be 

 deduced from the Laplacian law of density, and which is repre- 

 sented graphically by the broken line in Fig. 3. The ordinate 

 of this curve gives the ratio of the ellipticity of a stratum to the 

 ellipticity of the surface. It will be observed that the ellipticity 

 of strata near the center is about 80.72 per cent, of the 

 surface value. The actual case, then, does not differ from the 

 assumed case of uniform ellipticity by a very large amount. It 

 leads to the result that the change in pressure at the center of 

 the earth due to a change in the ellipticity of the outer crust, is 

 nearly the same in amount as if the earth were homogeneous, 

 although the percentage change is much less than in the latter 

 case. The relation between the ellipticity of any stratum to 

 surface ellipticity is given by the equation : 



