GRAVITATIONAL METHODS 



287 



from the dome the influence of the shallow dense cap may become ineffect- 

 ive; the gradients may reverse and be directed away from the dome because 

 of the influence of the deep-seated, lighter salt. For stations immediately 

 above the dome itself, in both cases, the gradients may be weak and erratic 

 as indicated in the figures. 



As illustrated in the preceding simplified examples, the gradient points 

 toward the higher structural position of a subsurface heavy mass. The 

 length of the gradient vectors is directly proportional to the slope of the 

 subsurface heavy mass or, more definitely, to the slope of the contact plane 

 of heavy and light material in the subsurface. It is also proportional to the 

 density contrast between heavy and light material on the two sides of this 

 contact plane. 



Two hypothetical cases will yield no gradient : ( 1 ) where there is no 

 slope to a density contrast plane in the subsurface, and (2) where there is 

 no density contrast in the section of rock below the surface, even though 

 the beds might have a slope. 



Curvature Quantity or R - line Value. — The torsion balance mea- 

 sures another feature relating to the configuration of subsurface masses 

 called the curvature quantity or R - line value. It is known to the British as 

 the H.D.T. or horizontal directive tendency.f The R-line value, as will be 

 shown, reflects curvature conditions of equipotential surfaces of gravity. 



RADIUS OF 

 CURVATURE 

 IS SMALL 



SECTION OF MAXIMUM 

 CURVATURE 



SECTION OF 

 MINIMUM CURVATURE 



Fig. 146. — Sketch of sections of a 2-axial ellipsoid, or football, showing rela- 

 tion of curvature and radius of curvature « of sections, taken at right angles 



to each other. 

 p max =^ maximum radius of curvature = section of minimum curvature, 

 p min =: minimum radius of curvature = section of maximum curvature. 



The latter may be illustrated by a two-axial ellipsoid, such as a football. 

 The curvature of the section through the long axis of the football is small. 

 The curvature of such a section is inversely proportional to the radius of 

 curvature (p). The section referred to, therefore, has a large curvature 

 radius. This is shown in Figure 146. 



The curvature of the section of the ellipsoid taken along a mid-perpen- 

 dicular at right angles to its long axis is large, and its radius of curvature 



t Edge and Laby, Geophysical Prospecting, Cambridge Univ. Press, 1931. 



