242 ANNUAL. REPORT SMITHSONIAN INSTITUTION, 1923 



rials must harmonize; and (4) seismologic data from which the 

 elastic constants of the materials in the interior may be computed. 

 These facts, together with the elastic constants of various rocks as 

 measured by the authors, 2 provide the basis for the present estimate 

 of the density and composition of the earth at various depths. 



The bearing of the above classes of data on the constitution of 

 the earth's interior will first be discussed briefly. 



MEAN DENSITY OF THE EARTH 



The constant of gravitation from direct experimental observation 

 is known to be 6.66X10— 8 cm 3 /g.-sec. 2 . This fixes the average density 

 of the earth at 5.52; that is, the earth is five and one-half times as 

 heavy as an equal bulk of water. This fact alone allows certain 

 qualitative inferences to be drawn concerning the interior. Tho 

 average density of the surface rocks is about 2.7 and no ordinary 

 rock has a density much above 3; therefore in all probability the 

 density near the center must be considerably higher than 5.5 in order 

 that the average density of the whole earth may have the correct 

 value. The precise manner in which the density varies with depth 

 and the magnitude of the central density are questions which long ago 

 attracted the attention of geophysicists. Several empirical laws have 

 been proposed for representing the density at a given distance from 

 the center of the Earth. Among the best known are those of 

 Laplace 3 and of Roche, 4 either of which, with an assumed surface 

 density 2.7, indicates that the central density is somewhat above 10. 

 These empirical " laws," of course, can not be expected to give a true 

 representation of density in the interior; the supposed continuity of 

 density change from the surface to the center, and the magnitudes 

 of the densities at various depths, rest upon insecure hypotheses. 

 Yet it is an interesting circumstance that either law, as will be 

 shown later, affords a rough qualitative indication of the earth's 

 density at various depths. 



The high density at the center obviously may be due either to the 

 presence of heavier material, presumably iron or nickel-iron, or to 

 a diminution of volume by the tremendous pressure existing at 

 great depths — or both factors may enter. It has often been as- 

 sumed that the increase of density with depth is merely the result 

 of the compressibility of the homogenous material. If this were true, 

 Laplace's law, for example, could be used to calculate the compressi- 



» Journ. Franklin Inst. 195, 475-529. 1923. 



sin qr 



* Laplace's equation, also derived independently by Legendre, is p=p<> —t*- in which p is the density at 



any distance r from the center, p is the central density, and g is a constant determined by the known total 

 mass of the earth. * 



* The law of Roche is p=/> (1— fcr»), in which ft is a constant which also can be determined from the earth's 

 total mass or mean density. 



