GRAVITATIONAL METHODS 



309 



sents an increase of about 1 X 10"^^ part of the value of gravity force. 

 The usual size of gradients measured in field exploration ranges, on the 

 average, from about 5 to 35 Eotvos units. 



The angle e is the difference in the direction of gravity at two points, one dh cm. 

 above the other. Taking the sensitivity of the torsion balance as 1 • 10"" c.g.s. and dh 

 as the distance between the upper and lower weights = 60 cm., it follows that the 

 divergence of equipotential surfaces which can be measured with the instrument is of 

 the order of 1/100,000 of a sec. of arc. 



_dh dg_ . _ 60 , ^ 

 ^~ g ' ds ' ^ ~ 1000 



€ is in radians ; 1 sec. = 4.8 • 

 6' 10- 



■ 4.8 • 10-'= 



^ 1 • 10-^ sec. or 



■ 10-" = 6 • lO-'' 



10-' radians. 

 1 



10-" = 6 • 10-" 



100,000 



of a sec. 



Forces Acting on the Torsion Balance Due to the Curvature 

 of Equipotential Surfaces 



Equipotential surfaces, of gravitational potential are characterized by 

 their curvature. A torsion balance is acted upon by components of the 

 gravity forces existing in a horizontal plane 

 which touches a curved equipotential surface, 

 as shown in Figure 171. 



There is no restriction on the shape of 

 an equipotential surface. However, within 

 the small portions of such a surface occupied 

 by a torsion balance, it is assumed that a 

 linear variation of gravity with distance 

 exists, and that the shape of the surface can 

 be completely represented by two radii of 

 curvature in two directions at right angles 

 to each other. These two radii have the 



property of representing the maximum and minimum possible radius of 

 curvature. 



A curvature of an equipotential surface is designated as positive if the 

 center of curvature is toward the earth's center from the surface, and 

 negative if the surface is convex toward the earth. This corresponds to 

 the general case of an anticline and a syncline respectively. 



When the torsion balance curvature efifects for certain types of sub- 

 surface mass configurations are computed, the curvatures may change along 

 a traverse, from positive to negative. This represents a reversal of direction 

 by 90° for the direction of the plotted R-line value (see Figures 147 to 

 149). 



The curved equipotential surfaces arising from local subsurface struc- 

 tures (such as an anticline) are superimposed on the larger equipotential 

 surfaces of the general gravitational field of the earth. Hence, although the 



Fig. 171. — Showing components of 

 gravity forces in a horizontal plane, 

 containing a torsion balance beam, 

 which touches a curved equipotential 

 surface. 



