256 



GRAVITATIONAL METHODS 



[Chap. 7 



K. Jung has published a number of diagrams showing the effects of 

 spherical masses on gradients and curvature values (see Fig. 7-96a). 

 If C (= curvature) is an abbreviated notation for —V'c/2kb and G 

 (= gradient) for Uxz/2kb, then the depth, D, to the center of the sphere is 



D = 2xq = 1.23xc 



max. ' 



its radius is 



) (7-926) 



E = 0.949 V^C,„ax.-2) = 0.823 \/G„ax.-i). 



For cylindrical disks, cones, and paraboloids of rotation"^ the curvatures 

 and gradients for points on the axis are zero. Lancaster-Jones"* has 



Fig. 7-966. Rectangular unsyraraetrical slab. 



calculated the gradients and curvatures of a vertical line element and of 

 a thin cylinder in order to arrive at a correction for the influence of trees 

 in densely wooded country. For the development of graphical interpre- 

 tation diagrams, the following relations for rectangular slabs are of im- 

 portance. If in Fig. 7-966 Zi is the depth to the upper surface, zi the depth 

 to the lower, X\ the distance to the south, and X2 the distance to the north 

 face of a rectangular slab whose extension in the strike is given by t/i 

 toward east and y^ toward west, and if distances to the corners are indi- 

 cated by numerals 1 to 4 in the east and by 5 to 8 in the west, integration 

 of eq. (7-91a) results in 



"2 Handb. Exper. Phys., 26(3), 160-161. 



1" Ibid. 



"< A.LM.E. Geophysical Prospecting, 508-509 (1929). 



