222 



GRAVITATIONAL METHODS 



[Chap. 7 



For sixteen and thirty-two azimuths, the formulas are calculated in the 

 same manner.^^ The final terrain formulas then take the following form 

 in Schweydar's first method : 



U^^ = ~ [2.36ci + 0.643C2 + 0.239c3 + 0.082c4 + 0.0186c6 



+ 0.00467C6 + 0.00187C7 + 0.001204c8 + 0.000803c9 

 -I- 0.0004284cio •.••] 



Uy» = I [2.366i + 0.64362 + 0.23963 +•..•] 



-U^ = ^[3.302ei + 1.96262 + 1.343e3 + 0.844e4 + 0.357e6 



+ 0.14766 + 0.080567 + 0.068668 + O.O6I669 

 + 0.0472610 ....] 



2t^x„ = ^[3.302dx + 1.962d2 +••..]• 



(.7-77) 



In these formulas the indexes of the Fourier coefl&cients refer to the 

 following distances (in meters): 



12 3 



9 10 



1.5 I 3 1 5 I 10 I 20 I 30 I 40 I 50 I 70 1 100 m 



The formulas are calculated for an elevation of 90 cm of the center of 

 gravity of the beam above the ground. The constants give the terrain 

 effects in E.U. Formulas for other beam elevations are given in the Aska- 

 nia publication referred to previously. 



Table 32 represents the calculation of a terrain correction in accordance 

 with eqs. (7-76) and (7-77). Above are the ground elevations in reference 

 to the height of the base plate (22.5) and the telescope axis of the alidade 

 (125 cm). With formula (7-76), the coefficients a, b, c, and d are cal- 

 culated and multiplied by the factors in (7-77) to obtain the effects of each 

 ring, whose sum gives the gradients and curvatures. The form represented 

 by Table 32 is used together with the form given on page 200 and con- 

 tains also the calculation of final results with planetary and terrain cor- 

 rections. 



Schweydar's second method is applied when the elevations of the sur- 



** C. A. Heiland, Directions for the Askania Torsion Balance; also A.I.M.E. 

 Geophysical Prospecting, 533 (1929). 



