THE STRENGTH OF THE EARTH'S CRUST 465 



distance ££' from epicenter to the traverse line is y. Then the 

 co-ordinates of any point on the surface are x, y, and D. At any 

 such point the component in the horizontal plane of the gravitative 

 force due to the outstanding mass is Fh. But Fh is directed radially 

 from all points to the epicenter. Fh, consequently, is subdivided 

 into two components at right angles. Let that acting in the line 

 of the section be called Fx, that at right angles be called Fy, parallel 

 respectively to the X and Y axes. 



The value of Fx for any point is given by the equation 



Fx=dc-irR^ 



3 {x'+y^+D^y^ 

 and the value of Fy is given by the equation 



Fy=dc-TrRi- y 



3 {x^-^-y^+D'Y'^ 



Fig. II shows the results of the solution of these equations. 

 In Fig. II A is drawn a contour map of the deflection force produced 

 by the unit sphere. The deflection force Fh at any point is measured 

 by the contour map and is directed toward the epicenter. The 

 lines of equal deflection are seen to be circles with center at E. 

 They show in plan the values which were shown in section by the 

 full lines for Fh in Figs. 9 and 10. The contours, as previously 

 discussed, are seen to give the form of a volcano whose crater has 

 a rounded rim and a conical interior reaching to the epicenter. 



Now let a number of parallel sections be taken at horizontal 

 distances from the epicenter equal to o. oD, o.$D, etc. The curves 

 for Fx for each section are shown in Fig. iiC and for Fy in Fig. 

 iiD. The points of maximum value for each section are indicated 

 in A, B, C, and D and through these points are drawn the curves 

 which are loci of maxima. For Fy there is a single maximum for 

 each section and this is situated at x = o. For Fx there are in 

 each section two equal maxima but of opposite sign, one for a 

 plus, the other for an equal minus value of x. In Fig. iiC only 

 one side of the curve is shown, that for plus values of x. 



Fig. iiB shows the points giving maximum values of Fx pro- 

 jected onto the vertical plane passing through X-X. The dip 



