244 ANNUAL REPORT SMITHSONIAN INSTITUTION 1923 



crease toward the center, in harmony with the inference already 

 drawn from the high density of the earth as a whole. 



THE ELLIPTICITY OF THE EARTH 



The earth, as is well known, is not a true sphere, but is flattened at 

 (he poles, approximating very closely to an ellipsoid of revolution. 

 The ellipticity, or flattening, is about 1/297 ; that is, the polar diame- 

 ter is 1/297 less than the equatorial diameter. Now the amount of 

 of this flattening depends upon the way in which the density varies 

 within the earth. Thus, if the earth were of uniform density the 

 flattening would be 1/232. But although it might seem that the 

 flattening would provide an independent means for determining the 

 density distribution within the earth, it so happens that a distribu- 

 tion which will satisfy the moments of inertia about the two axes 

 will yield almost exactly the right value for the ellipticity. 7 



TRANSMISSION OF EARTHQUAKE WAVES 



Perhaps the most useful source of information concerning the 

 earth's interior is furnished by the velocities with which earthquake 

 shocks are transmitted through the earth. It has been shown from 

 the theory of elasticity that any disturbance in a sphere of elastic 

 isotropic material should give rise to various kinds of waves travel- 

 ing with velocities depending only on the density and elastic con- 

 stants of the material at each point. Waves of two of these kinds 

 would pass through the sphere, while the others, which are less 

 simple to analyze, would travel over the surface. A seismograph 

 recording the time of arrival of the various waves at some other 

 point would show the arrival first of the two waves passing through 

 the earth and later that of the various surface ones. One of the 

 " through waves " consists of transverse vibrations, while the other 

 consists of longitudinal vibrations and travels with a higher ve- 

 locity. 8 These through waves should theoretically be easily dis- 

 tinguished from the surface waves by the circumstance that their 

 apparent velocity (i. e., the velocity obtained by comparing their 

 times of arrival at various points on the surface with the corre- 

 ponding distances from the origin) should vary with the distance, 

 whereas the velocity of the surface waves should be constant. The 

 records of earthquakes as obtained by sensitive seismographs reveal 

 these expected features, and we may with considerable confidence 

 use the theoretical relations between velocities and elastic constants 

 to calculate the rigidity and the compressibility of the material 



'Of. W. D. Lambert, The internal constitution of the'earth. Journ. Wash. Acad. Sci., 10, 127. 1920. 

 •The velocities of the transverse and longitudinal waves are respectively: Va=-JRIp and Tp= 

 ■J(K+4R13)[p, p being the density, R the rigidity, and K the bulk modulus. 



