THE STRENGTH OF THE EARTH'S CRUST 463 



The summation of this discussion shows that if in the first 

 assumption as to the form of abnormal masses they be taken as 

 spheres, then the determination of the depth of the center of mass 

 by means of the curve for Fh and the location of the point of maxi- 

 mum value is more likely to overestimate than underestimate 

 the depths and masses. As the object of this investigation is 

 especially to find the depth of masses and to test the hypothesis of 

 centrospheric heterogeneity as a cause of deflection residuals and 

 gravity anomalies, it is desirable to have the error of interpreta- 

 tion in the direction of indicating a depth too great rather than 

 too small. Therefore the initial assumption that the outstanding 

 masses are spheres is justified by the geologic probabilities and is 

 found in Section B to be justified by the geodetic evidence. The 

 next topic will therefore develop further the subject of the interpre- 

 tation as spheres with the view to utilizing the geodetic data. 



Depths of spheres whose epicenters are not on the line of traverse. — 

 If the primary purpose of a geodetic investigation were the deter- 

 mination of the location of the epicenters of abnormal masses and 

 then the measurement of their form, size, and depth, a series of 

 gravity and deflection measurements could be made in a line passing 

 above the mass and near the epicenter. The preceding discussion 

 would then directly apply. In only a few locahties, however, will 

 a line of triangulation stations, located in connection with the 

 measurement of the earth's surface, pass approximately over the 

 center of a large outstanding mass. How then, from the locations 

 and values of the deflection force along any linear belt of measure- 

 ments, shall the locatipn of the epicenter and depth to the center 

 of an abnormal mass to one side of the line of traverse be deter- 

 mined ? 



In Fig. 1 1 is developed a method for the solution of this problem. 

 In accordance with the preceding discussion and the reconnaissance 

 nature of a first investigation, let it be assumed that isolated 

 abnormal masses approach a spherical form; that is, that a mass 

 may be regarded as concentrated at a point. Take the center of 

 the mass as the center of co-ordinates and the axis X-X as lying 

 parallel to the line of traverse. The epicenter is at E. Then the 

 vertical distance from the center to the epicenter is D. The 



