THE STRENGTH OF THE EARTH'S CRUST 459 



magnitude as the more distant ones and therefore the effects of 

 the distant masses sink to neghgible quantities in comparison, in 

 accordance with the law of inverse squares. The general agree- 

 ment in the magnitude of the departures from isostasy, as shown 

 by deflection residuals and gravity anomalies, shows, furthermore, 

 that deep nucleal heterogeneities can have no large and broad 

 regional effects, since such would affect the gravity measurements 

 within a broad central circle to a greater degree than they would 

 the deflections of the vertical. Therefore each region is seen to 

 offer its local problems and the dominating centers of outstanding 

 masses may be readily determined save where several such masses 

 are contiguous, especially if of opposite sign. Let attention be given 

 then to those features in the influence of outstanding masses which 

 are indicative of the form and depth of the attracting mass. 



Let the depth to the center of mass be D. Then it is seen that 

 for ellipsoids near the surface in which the major axes are twice 

 the minor axes the influence of form has mostly disappeared at 

 horizontal distances from the epicenter or from 2D to 3Z), and at 

 greater distances the curves become practically coincident. For 

 greater departures from the spherical form the distances before the 

 curves approach those given by a spherical mass are still greater. 

 At these distances where the curves approach those of spheres, 

 the effects of the form of the mass could not be distinguished, but 

 the curves are so flat that neither could the effects of depth be 

 readily evaluated. For instance, the curves of force at 4D to 6D 

 for a sphere of mass M at depth D would be approximately the 

 same as for a sphere of mass 4M at a depth of 2D. Furthermore, 

 at these distances from the epicenter the forces are so small in 

 proportion to the maxima for the same mass that other outstanding 

 masses would greatly change their value and prevent a correct 

 analysis. Therefore, to be determinative, observations must be 

 made at a number of points between the epicenter E and a distance 

 not more than double that which at the point M gives the maximum 

 value to Fh. It is seen that if a mass symmetrical about a vertical 

 axis departs widely from the spherical form, this will be detected 

 by noting the ratio of maximum Fv to maximum Fh, the latter 

 being measured along any line radiating from the epicenter. If 



