466 JOSEPH BARRELL 



angle 6 measures the slope from the point of maximum value to 

 the center of mass. Here is shown its value when projected onto 

 the plane X-X. This projected angle is seen to grow smaller with 

 each more eccentric position of the section plane. 



For section o.oD the real value of ^ is 55° 

 For section i . oD the projection of 6' is 45° 

 For section 2.0D the projection of $" is 32° 

 For section 3 . oD the projection of 6'" is 24° 



Therefore it is seen that if the traverse hne were assumed to pass 

 through the epicenter of all disturbing masses, the error introduced 

 would be to show the center of mass deeper than it really is. The 

 nature, however, of the geodetic data permits this assumption to 

 be eliminated and the distance EE' to the section plane to be 

 approximately determined. An error up to 0.5D will not involve 

 much error in the resultant depth as determined by the projection 

 of d. At each station along a line of triangulation"^ both Fx and 

 Fy are determined and their resultant points toward the center of 

 gravitative control. Each station gives an independent deter- 

 mination of this resultant and the intersection of two resultants 

 if accurately determined and due to the gravitative force of a single 

 symmetrical mass would give an accurate location of the epicenter, 

 measuring its distance and direction from the traverse line. The 

 data in many cases permit as many as three or four resultants to 

 be drawn, the size of the triangle of their mutual intersections 

 showing to what degree the forces may be ascribed to a single 

 center. The relative positions of the line of section and epicenter 

 of mass are thus in many cases approximately established. 



But although the relative position of epicenters and traverse 

 line are thus ascertained, the depth of the masses remains to be 

 solved. In Fig. 11 the distance of the traverse line from the epi- 

 center is given in terms of D, but this is the unknown. Two inde- 

 pendent methods lead up to the solution of D. 



First, on any line of section occurs a zero point for Fx. Let 

 this be called E'. On each side of the zero point for Fx occurs a 



^ As shown in illustration No. 3, Hayford, Supplementary Paper. 



