TABLE 839.— CHARACTERISTICS OF EARTH'S INTERIOR* 739 



Part 1. — Density and pressure 



The density distribution in the earth's interior is obtained by a series of approximations 

 made to conform with known data as boundary conditions. These known facts, with which 

 any density distribution must harmonize, include the following : 



(1) The average density is 5.522, obtained by comparing the attraction of the earth 

 with that of a known mass. Dr. Heyl's value for the constant of gravitation is used, 

 6.664 X 10- 8 dyne cm 2 g~ 2 (Table 27). 



(2) The precession constant and other astronomic and geodetic data (Table 827) give 

 the earth's moments in inertia. / = 0.33344 Er 2 where / is the moment of inertia about 

 the polar axis, r the equatorial radius, and E the mass of the earth ; further 



1 =&/*<-) 



where a is the polar semi-axis and p=r/(a,r), the density. If the earth were a homoge- 

 neous sphere its moment of inertia would be 0.4 Mr 2 and density 4.6. 



(3) The known flattening of the earth from geodetic data is 1/297. If the earth were 

 homogeneous the flattening would be larger. These should be sufficient to give a unique 

 density distribution but, as Lambert of the Coast and Geodetic Survey pointed out, a 

 distribution satisfying condition (2) also satisfies condition (3). 



(4) The last boundary condition results by comparing the elastic behavior at various 

 depths with the known elastic constants of rocks. Time-distance curves of earthquake im- 

 pulses enable one to calculate the velocities of the compressional, V 9 , and distortional, V '«, 

 waves at various depths in the earth. Assuming isotropy there are simple relations between 

 K, R, E (moduli of compression, rigidity, Young's respectively), a (Poisson's ratio), V P 

 and V s such that if the density and any two of them are known the others can be had. The 

 variation in elastic constants for different rocks is small but sufficient to permit discrimina- 

 tion when compared with the elastic properties at different depths computed by means of 

 the equations 



V, 2 = R/ P , V p 2 -teV. s = K/p, (V p /V,) 2 = 2 . (l ~ ff) 



The uncertainties result from extrapolating low pressure and temperature laboratory data 

 to high pressures and temperatures. 



Whence we deduce : "granitic" material to a depth of 10 to 30 km ; below this the rock 

 is denser, about 3.0, and corresponds to a basalt or gabbro. At about 45 km depth a dis- 

 continuity occurs ; the change in elastic properties corresponds with a transition to peri- 

 dotite, density 3.4. From this depth to 1,600 km the variation is uniform, the density in- 

 creasing slowly with pressure. From 1,600 to 2,900 km the earthquake velocities remain 

 somewhat constant and could be accounted for by a slow addition of iron and nickel to the 

 material, the density changing from 3.4 to 9.0. Below # 2,900 km V P begins to decrease 

 slightly and the assumption is that this core consists of' nickel-iron with a density at the 

 center of about 10.7. 



SMITHSONIAN PHYSICAL TABLES 



