Chap. 7] 



GRAVITATIONAL METHODS 



189 



It is seen that from the diametrical positions 1-3 and 2-4, the gradients 

 alone may be obtained, but that for curvatures an additional intermediate 

 position is required. 



Hence, for the gradients, 



Uxz = -~ — 7x(a'/_3 - Ai'ls), and 



2b>/3 



C/v. = 



1 



''' ~ 2b '-" 



or 



Uzz = -^-Aa^, and 

 2b 



C/.. = - 



2b V3 



(A2-4 — A2_4). 



• (7-57a) 



From combinations 1, 3, 4, and 6, we have the following equations for the 

 curvatures : 



(1) 



(3) 



(4) 





(6) 



U.= 



2a 



1 



2a\/3 



{^U-^!;U)-~{U.Z- Uy.) 



2U.y = ^- A3-. + ^ (C/XZ + f/..) 



(7-576) 



Although it is not a gradiometer, the continuously rotating balance 

 proposed by Kilchling*" may be mentioned here. It consists of a single 

 combined gradient and curvature balance, which is suspended from a 



80 K. Kilchling, Zeit. Geophys., 2(4), 134-137 (1926); 3(6), 281-285 (1927). 



