542 JOSEPH BARRELL 



of mass is close to the surface. It may be any value less than 40 

 per cent of maximum Fy, according to the depth of the center. 

 But having chosen that ratio which appears to fit the demands of 

 the data, the distance of the point of maximum Fx from the point 

 of zero value becomes also fixed. The curves numbered 2 in Figs. 

 12B and C must therefore satisfy between them the demands of the 

 ratios shown in Figs. iiE and F. The value of EE' as deduced 

 from either curve must be the same. 



The sum of all the Fy curves in 12B is marked S Fy and must 

 pass through, or close to, the points which measure the values 

 given by the deflection residuals. These points are shown as small 

 rectangles in B and C and give ordinates which correspond with 

 the size of the components of the residuals as shown in A. In 

 drawing B and C the adjustment of the curves to give the proper 

 values to S Fy and S Fx resulted in a slight readjustment of the 

 centers of mass as shown in A. The positions as shown in Fig. 12A 

 have been determined from the curves below, and their approximate 

 agreement with the initial indications of the resultants is a check on 

 the validity of the solution. It is seen that the epicenter of a mass 

 should not lie on the exact intersection of any two resultants, 

 since at the point of measurement several masses have an appreci- 

 able influence upon the direction of the resultant. The adjustment 

 of the curves is therefore the best way of determining finally the 

 best location of the epicenters. 



The measurement of these curves gives the tabulation of data 

 shown in Table XXVIII. 



The depth to the centers of the equivalent spheres having been 

 solved by means of the ratios given in Figs. iiE and iiF, the masses 

 of these spheres are ascertained as follows. In Fig. 1 1 the value of 

 the maximum deflections for Fy and Fx due to the unit sphere are 

 shown for various distances of the section line from the epicenter. 

 For example, for EE'=i.^D, max. Fy is 4.6''. Now for sphere 

 No. 4, Fig. 12A, ££'=1.504 and the max. Fy is 6.2''. But D 

 for the unit sphere is 64 km. whereas D^ is 7,1 km. Now the magni- 

 tude of the deflections for points similarly situated in two fields of 

 gravitative force will vary directly as the respective masses and 

 inversely with the squares of the distances. This may be put into 



