206 



GRAVITATIONAL METHODS 



[Chap. 7 



Table 27 



CALCULATION OF FIVE-POSITION TORSION-BALANCE RECORD 



(FROM A's) 



Part 1 



Beam II: Beam I: 



A^ + a; = +13.3 A^' + A5' = -41.2 A3 + a1 = +17.5 A2 + As = -42.0 

 Ai" - A? = +13.5 Af-A^' = -23.2 A4-A5=+26.1 A^ - A^ = -2.2 



Table 28 shows the calculation of gradients and curvature values for 

 each beam from the sums and differences in Table 27, in accordance with 

 the formulas given on page 184. The same numerical coefficients apply 

 to the calculation of gradients and curvatures from the n's as from the 

 A's. The calculation is shown in Tables 29 and 30. Table 31 contains a 

 summary of results obtained for both beams combined or individually in 

 three, four, and five positions. 



5. Operation of torsion balances. First, an observation site that is flat, 

 at least in the immediate vicinity, should be selected. Next, the differences 

 of elevations on concentric rings are measured at eight or sixteen points, as 

 described in the next section. Three wooden stakes are driven into the 

 ground, and their tops are leveled and placed at an elevation such that the 

 center of gravity of the beam is at a height for which the terrain correction 

 has been calculated. A base plate is so laid on the wooden stakes that its 

 north groove points north, and the differences in elevation for the inside 

 terrain circles against it are determined. It is advantageous to set out a 

 stake about ten feet north of the station site to facilitate orientation of the 

 base plate, house, and instrument. After the hut is erected, the instrument 



