THE STRENGTH OF THE EARTH'S CRUST 467 



maximum value for Fx. Let the point of this maximum be called 

 M. These two values are given by the geodetic data. Then for 



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 any spherical mass the ratio of WJ7 increases with increase in the 



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ratio of —jz- but not as a rectilinear function. This relation of 



ratios is shown graphically in Fig. iiE, in which the abscissas are 



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 the values of -j^ and the ordinates are the corresponding ratios 



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 of jpfi,j - This ratio may be determined from the geodetic data 



but from the location of the maxima, not their amount. 



The second method for determining the depth depends upon 

 the ratio of the maximum value of Fy for any traverse line to the 

 maximum value of Fx for the same traverse line, thus being depend- 

 ent upon the relative values of the maxima and not their location. 



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 This ratio also increases with increase in the ratio of —j^ but not 



as a rectilinear function. The maximum Fx for a section at any 

 distance from E is shown in Fig. iiC. For example, if E'E = 

 o . 5Z) the maximum Fx for the unit sphere is 5 . 52". The maximum 

 Fy is shown in Fig. iiD, and for E'E = o. 5Z) is 6.42". The ratio 

 of 5.52 to 6.42 is 1. 16. These ratios are shown in Fig. iiF 

 for all traverse lines up to a distance of 3 . oD from the epicenter. 

 The value of this ratio is given by the geodetic data for any 

 traverse Une and hence the distance to the epicenter is given in 

 terms of D. 



In conclusion on this topic it may be said that the curves shown 

 in Figs. iiE and iiF are independent of the mass or volume of 

 the sphere, depending only upon its depth, and are adapted to 

 use with the geodetic data. It is seen from both curves that the 

 significant ratios change in value rapidly with increasing distance 

 of the traverse line from epicenter up to a distance E'E^D, 

 but beyond this point the change in the value of the ratios be- 

 comes progressively small as compared to a change in the distance 

 of the section plane. The method is therefore well adapted for 



