Chap. 7] 



GRAVITATIONAL METHODS 

 Table 21 



187 



Fig, 7-63 shows the Numerov^' three-beam balance. 

 With it, gradients may be determined in" the 0" and 

 180° or 90° and 270° positions. An intermediate 

 azimuth is required for curvatures. The beam 

 azimuths and readings in these positions are shown in 

 Table 22. 



The equations for the six possible combinations 

 (canceling the torsionless-position reading) are:'^ 



(1) From positions 1 and 2: 



n[ — n^i = a(_2 = ^eJJxv + bC/„« + bf/„ 



ni' — na' = AiU = — 2aC/xy -}- a\/3 C/a 



+ ^(V3-l)f/« 



(\/3 + l)C/. 



ni 



rh 



4" = ^1-2 = -2a.U^ - aVs Ua 



-^(\/3 + l)C/v. + ^(\/3-l)t/, 

 Tablb 22 



Fig. 7-63. Nu- 

 merov - Askania 

 three-beam bal- 

 ance. 



" B. Numerov, Astron. Inst. Leningrad BulL, 30, 103-108 (1932). 

 "« For simplicity, the constants a and b are 'here taken to be alike for all three 

 beams. 



