THE PRESSURE WITHIN THE EARTH 69 



to the value of the pressure at the intersection of the equipo- 

 tential surface with the polar and equatorial radii. 



The pressures for e = .4 are not shown in the diagram, but 

 they are not greatly different from those shown for ^=.5. It 

 should be noticed that the pressures for £ = .5 are about 8 per 

 cent, less than for the spherical form, and for e=.4 the pressures 

 are about 5 per cent, less than for the spherical form. 



The results above given were worked out on the supposition 

 that the spheroid was homogeneous, having its density equal to 

 the mean density of the earth. Of course the actual spheroid is 

 not homogeneous, but heterogeneous, with the density increasing 

 from surface to center. We know that the density of the surface 

 material of the earth is approximately 2.75, and that the mean 

 density is about twice as great. The exact law of variation of 

 density in the interior cannot be said to be known, yet the law 

 assigned by Laplace nearly a century ago is generally accepted 

 as close to the truth. This law of density is as follows : 



4.365 a . 2.4605 a 



p= sin — ; 



a a 



in which p is the density of the stratum whose mean radius is a, 

 the mean radius of the surface being a . The numerical constants 

 are determined on the supposition that the surface density is 2.75 

 and the mean density twice as great. The variation according 

 to this law is shown graphically by the heavily drawn curve of 

 Fig. 3. An inspection of this diagram shows that the density 

 increases quite uniformly for a considerable distance as we pass 

 from the surface towards the center. We finally come to a cen- 

 tral nucleus of nearly uniform density. The density at the center 

 is 10 : 74. 



The Laplacian law of density agrees well with the measure- 

 ments of precession, and is probably as near to the truth as the 

 measured values of the earth's mean density. 



An exact method for determining the pressures within a 

 heterogeneous spheroid without knowing its rotation period is 

 not known to me. Even if the rotation period of the heteroge- 



