258 



GRAVITATIONAL METHODS 



[Chap. 7 



C/x'. =^k8 



,.SVsin2.f;i^«a..S.^^^[l-|©V....] 



/+6 7 2 

 — 



2 2 



p COS (p 



db 



= 2fc5.dS 



■^-^T^+L-r^I. ©+••••]• 



(7-92e) 



When the extension of the Une is ±00, the second terms in the brackets 

 vanish and the two-dimensional values as given in cq. (7-916) remain. 

 Hence, these terms indicate the error committed when limited features 

 are considered two-dimensional. According to Jung"^ an error of 1 per 



6raditnh 5 4321 12345 mtfers Curvoturts 



5 '5.64m'; <f--1 



Fig. 7-97. Effect of two-dimensional mass (cylinder section) on gradients and curva- 

 ture values (after Jung). 



cent is produced in gradients when h is less than 2.5p, and the same error 

 arises in curvatures when h is less than 12p. For gradient calculation it 

 is therefore permissible to consider most geologic features of elliptical out- 

 line as two-dimensional in interpretation calculations. 



As an example of a two-dimensional feature, consider the torsion balance 

 anomalies due to a horizontal cylinder. These anomalies follow directly 

 from eq. (7-9 Ic) and are 



and 



U,, = 2k5R\'^^. 



> (7-93a) 



"OHandb. Exper. Phys., 25(3), 184 (1930). 



