Chap. 7] 



GRAVITATIONAL METHODS 



199 



read conveniently, the sensitivity for curvatures is proportional ^HK/vt 

 and for gradients 20tm,hl/vT, where for double reflection the factor 40 

 takes the place of 20. The reciprocal of the sensitivity is the "scale 

 value" of the instrument, 



20fmhl 



(gradients) and 



€c = 



20iK 



(curvatures) (7-62) 



where 40f instead of 20f is used for double reflection. 



4. Calculation of instrument readings of a standard torsion balance 

 proceeds in accordance with formulas (7-526) to (7-545). A number of 

 positions are generally repeated. Deflections are averaged in such a 

 manner that the variation of the torsionless position with time is elimi- 

 nated. In visual torsion balances, beam readings are entered against 



Fig. 7-70. Evaluation of torsion-balance record (large Ask&nia balance). 



azimuth, time, and temperature (see Fig. 7-71). Calculation is the same 

 as in photographic balances. Fig. 7-70 illustrates a record taken with a 

 recording balance. On the left is the fixed mirror record, then follows 

 the record of the second balance, first balance, and temperature. For 

 evaluation, a graduated scale is placed over the record and its 0-line 

 aligned with the fixed-point line. Deflections for positions occupied are 

 read for beams II and I, giving Ui, n^, Uz, Wi, n^, and na, and so on, in 

 scale divisions. These are entered for three positions in Table 23. The 

 temperature record is not evaluated. The torsionless position is calcu- 

 lated by averaging successive readings in the following manner: 



1. no = \{ni + ^2 + W3) 1. W 



2. no = \{n2 -\- n'z -\- n\) 2. no' 



3. no = \{n[ + n{ -}- na) etc. 3. rio 



If II . II . 11^ 



t(ni + n2 + ns ) 



\{n^ -f- ns + ni) 



\{ni -f n'l' -f- n^') etc. 



