186 



GRAVITATIONAL METHODS 



[Chap. 7 



/ 



Fig. 7-62a. Haalck bal- 

 ance (gradiometer). 



If two balance systems are used in a gradiometer, 

 only two azimuths are required. 



In the Haalck totsion balance (see Fig. 7-62a) 

 two standard beams are used at right angles to 

 each other; only two azimuths are necessary to 

 cancel the curvatures and to determine gradients. 

 The arrangement is seen from the following 

 scheme : 



Balance I Balance II 



Reading • Reading 



Azimuth 1, a = 0°. n[ a = 90°. 



2, a = 180°. no a = 270°. 



With formula (7-516) 

 (position 1) : 



n[- 

 n'.' 



(1) balance I: n'l - n'o = a'-2C/^ +b'-f/y^, 



(2) balance II: n'/ - n'o = a". -2C;^^ + h"-U, 

 (position 2): 



(3) balance 1: n'^ - n'o = &'2U^ +b'.-t/„,, 



(4) balance II: n^ - n'o = a"- -2U:cy + h".-\-U, 

 Subtracting equation (3) from (1), 



and subtracting equation 2 from 4, 



Uxz = 2b"" ^^^' ~ ^'^^' 



Curvature values may be obtained by 

 setting up the balance in three azimuths. 



In Hecker's balance (Fig. 7-626), four 

 beams are used in such manner that two 

 standard sets make an angle of 60° with 

 each other. Only two azimuths are re- 

 quired to obtain both gradients and 

 curvature values. The formulas for this 

 instrument may be derived by substi- 

 tuting the values in Table 21 in eq. 

 (7-516). 



(7-56) 



jL^:r^_ 



Fig. 7-626. Hecker four-beam 

 balance. 



