224 



GRAVITATIONAL METHODS 



[Chap. 7 



Their variation with azimuth is again represented by Fourier series, so 

 that the new coefficients (comparable with those given in [7-71]) are: 



\B\ = -.J^H'sma and \C\=-^H' cos a (7-78) 

 m m. m m 



Instead of introducing again a linear variation between two rings, it is 

 now more convenient to assume a variation of their squares between 

 three rings, so that 



H = Ci + C2P -f C3P . 



The coefficients are determined from the variation of H' in one azimuth 

 in three distances, Pn, Pn+i, and Pn+2, so that the gradients 



U xz — "^ n 



da 



> (7-79) 



73/ Ci cos a 



f2T /•2r "1 



C2 COS a da -\- I2 j C3 cos a da 



\ h I Ci sin a da 



-2ir -2r ~1 



+ h I C2 sin a da + I2 I C3 sin a da , 



where the integrals /i, 1 2, and 1 3 are as given in (7-756) except that the limits 

 are Pn and Pn+j- Substituting numerical values for the same distances as 

 in the first method the gradient formulas of the second method are : 



[/„. = -3fc 



f/x. = - 5 [172.9 1 C li + 11.64 I C I2 + 17.92 | C I3 + 3.020 1 C i4 



+ 1.454 I C 1b + 0.031 1 C Is + 0.1404 1 C I7 

 + 0.0399 I C Is + 0.0592 1 C I9 + 0.0152 | C |io] 



(7-80) 



Uyz= - ^[172.9 |B|i+ 11.64 |Bi2+ ...•]. 



These formulas hold for f = 0.9 m. All elevation (differences) must be 

 expressed in meters. The formulas for curvatures originally given do not 

 change. Table 33 illustrates the calculation of terrain corrections for 

 both curvatures and gradients (second Schweydar method) for very rugged 

 terrain. Fig. 7-76 gives an idea of the magnitude of terrain effects under 

 such conditions. 



In concluding the discussion of analytical methods, brief reference should 

 be made to a method for calculating the effects of remote terrain features 



