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ANNUAL, REPORT SMITHSONIAN INSTITUTION, 1923 



density and velocity curves from which they are derived. This 

 means that from the surface to a depth at least halfway down to the 

 center the elasticity of the material increases regularly and steadily 

 in spite of the fact that the material changes in character, being 

 silicate rock near the surface and metallic iron farther down. 



At great depths the bulk modulus is very great, and therefore the 

 compressibility, which is the reciprocal of the bulk modulus, is very 

 small. Thus at a depth of 1,600 km. the silicate is nearly as incom- 

 pressible as diamond, which is the least compressible of any known 

 substance. 



Fig. 5. — The rigidity and bulk modulus at various depths below the surface as calcu- 

 lated from the densities and earthquake velocities. The rigidity is the resistance to 

 deformation, and the bulk modulus Is the resistance to compression and is also the 

 reciprocal of the compressibility 



The rigidity also is very high in the interior of the earth. From 

 the fact that the rigidity of steel is about 0.9 in the units used in 

 Figure 5, it may be seen that except near the surface the rigidity of 

 the earth is greater than that of steel. The rigidity is equal to 0.9 

 at about 400 km. depth and rises to five times this amount at 3,000 

 km. depth. Measurements 34 based on the tidal deformation of 

 the earth indicate that the effective rigidity of the earth for such 

 deformations is 0.86, which according to Figure 5 is the average 

 rigidity of the outer 800 km., or 500 miles. If, then, it be the outer 

 800 km. which takes part in tidal deformations, the agreement be- 

 tween the two entirely different methods of determining rigidity 

 would be complete. 



M A. A. Michelson. Astrophys. Journ. 39, 105-138. 1914. 



