310 



EXPLORATION GEOPHYSICS 



curvature of an equipotential surface due to a local structure may be 

 negative, the curvature of the total resulting surface may still remain 

 positive. This is analogous to the curvature effects on lines of force of 

 gravity from local heavy masses in the subsurface w^hen added to the 

 direction of lines of force of the earth's field, as in Figure 155. We are 

 entitled to consider the level surfaces from local subsurface structures and 

 their curvature by themselves, however, or as though their eflfect were not 

 superimposed on the general gravitational field, because we subtract the 

 influence of the latter in the "normal value" correction from the torsion 

 balance field readings. 



Two vertical sections (I and II) through a spherical equipotential 

 surface and the horizontal projections of gravity force in a horizontal plane 

 touching the surface at one point are shown in Figure 172. The actual 

 curvature radii are, of course, much larger than those illustrated. For the 

 gravitational field of the earth these radii of curvature are of the order of 

 the earth's radius, or some 4,000 miles. 



Fig. 172. — Showing vertical sections I and II taken at right angles to each other 

 through a spherical equipotential surface, and the projections of the gravity forces acting 

 in a horizontal plane which touches the equipotential surface at one point. Part B gives 

 the direction of the resultants of the components of force in the horizontal plane which 

 are straight lines converging toward the center. 



In sections I and II we have principal curvatures which are at right 

 angles to each other, and in this case equal. The resultant horizontal forces 

 for any part of the horizontal plane are obtained by combining the com- 

 ponents of sections parallel to section I and sections parallel to section II, 

 and then forming the resultants. 



Connecting the directions of these resultants gives the horizontal pro- 

 jections of the lines of force. These are straight lines which converge 

 toward the center of the figure, as shown in part b. Figure 172. There 

 would be no turning forces acting on a simple horizontal beam torsion 

 balance (with no hanging weight) suspended in such a field. The forces 

 would be acting along the beam in any orientation thereof. 



Figure 173 is similar to Figure 172 with the important exception that 

 section I in the N-S direction has a smaller curvature than section II in 



