240 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1916. 



The modulus of elasticity at each point in the earth controls the 

 behavior of the earth under relatively small applied forces. 



The strength of the earth, at each point, as measured by the stress- 

 difference at that point necessary to produce either slow continuous 

 change of shape or rupture, decides the behavior of the earth under 

 the greater forces applied to it. 



As to density we laiow that the earth's surface density is about 

 2.7, that the density probably increases continuously with increase of 

 depth, that the density at the center is probably about 11, that the 

 mean density is about 5.6, and that within a film at the surface of a 

 thickness of about one fiftieth of the radius of the earth there is 

 isostatic compensation which is nearly complete and perfect as be- 

 tween areas of large extent. 



The manner of distribution of the isostatic compensation with 

 respect to depth, and the limiting depth to which it extends are but 

 imperfectly known. Nevertheless it appears that above the depth, 

 122 Idlometers, the compensation is nearly complete even though 

 there may be some compensation extending beyond that depth. 



Two general lines of evidence are available in determining the 

 modulus of elasticity of the earth, that from earthquake waves, and 

 that from earth tides. 



There are many inherent and extreme difficulties in the way of 

 securing reliable evidence as to the modulus of elasticity from earth- 

 quake waves. 



To 1913 the accuracy of available observations of tides in the solid 

 earth was insufficient to furnish a basis for reliable conclusions. 

 Nevertheless the estimates of the modulus derived from these early 

 observations were a fair approximation to that given by the very 

 recent and much more accurate observations. 



Dr. Michelson and those associated with him in the observation of 

 earth tides at the Yerkes Observatory since 1913 have developed a 

 method of observing which is of a new order of accuracy such that 

 the minute changes of inclination at a given point due to earth tides 

 may be determined with an error of less than 1 per cent. 



These observations make the modulus of elasticity of the earth as 

 a whole about like that of solid steel, namely, (8.6) (10" C.G.S.). 



It is the modulus of elasticity of the earth as a whole which is 

 measured in this case. 



It is eminently desirable to determine if possible whether the 

 modulus of elasticity varies with increase of depth. The Michelson 

 apparatus possibly opens the way to such a determination. Suppose 

 that the apparatus is used on the shore of the Bay of Fundy. Twice 

 a day a large excess load of water is placed in the bay by the tidal 

 oscillation and as frequently the water load is reduced below normal. 

 The stresses produced in the body of the earth by these changes of 



