THE STRENGTH OF THE EARTH'S CRUST 449 



The sphere having the same volume as a cyHnder 122 km. in 

 radius and 122 km. in depth will have a radius of iii km. Let 

 a radius of 100 km. and a density of ±0.025 be assumed as the 

 dimensions and mass of a standard sphere in this deep zone. If 

 the center of such a sphere is at a depth of 183 km., the same depth 

 as the center of Gilbert's postulated cylinder, the anomaly at the 

 epicenter will be 0.021 dyne, whereas the cylinder gave an anomaly 

 of 0.023 dyne. They are therefore nearly equal in effect. If the 

 center of the sphere is placed at a depth of 319 km., making the 

 top at 219 km., the anomaly at the epicenter becomes 0.0068 

 dyne. Consequently the variation in density or volume of the 

 sphere would have to become three times as great in order that its 

 maximum anomaly should equal the mean observed anomaly. 

 But as the average anomaly is not measured at the epicenter, and 

 the maximum anomalies, occurring at the epicenters, are several 

 times the observed mean anomalies, this figure would have to be 

 still further multiplied. To account, therefore, for the magnitude 

 of surface anomalies, the disturbing spheres, if with centers at a 

 depth of 319 km. and if of 100 km. radius, would have to have 

 abnormalities of densities ranging up to 0.25 in order of magni- 

 tude. If the centers of the spheres were at twice this depth the 

 abnormalities, to produce the same eifect, would have to be four 

 times as great in mass. In a region of which there is no precise 

 knowledge such variations of density might well occur. The 

 problem must therefore be investigated by means of the gradients 

 which would result in the gravity anomalies and deflection residuals 

 and a comparison of these with the gradients actually observed 

 and plotted. 



Distribution of surface forces for centro spheric spheres. — For 

 masses as deep as these the curvature of the earth becomes of 

 importance, but the complications which it introduces into the 

 analytic treatment have been avoided by means of a graphic 

 solution. 



In Fig. 8A, the anomaly is calculated for the epicenter. Then 

 the gravitative force at any other point on the surface, such as 

 that having a dip angle d, can be determined by squaring the inverse 

 ratio of distance. Multiplying the force at the epicenter by this 



