210 



GRAVITATIONAL METHODS 



[CiiAP. 7 



Table 31 



D. Corrections 



After torsion-balance readings have been calculated in the form of 

 gradients and curvature values as shown in the preceding section, a number 

 of corrections must be applied. These may be divided into corrections 

 required for every station and corrections required only in special cases. 

 In the first group fall (1) the planetary correction, and (2) the terrain 

 correction; in the second are (3) corrections for regional effects, (4) cor- 

 rections for coast effect, and (5) corrections for fixed masses other than 

 terrain, underground openings, and so forth. 



1. Planetary corrections. As in measurements of relative gravity with 

 the pendulum or gravimeter, the normal or planetary variation of gravity 

 must be considered in both gradients and curvature values. It is here 

 again sufficient to consider the earth as an ellipsoid of revolution with a 

 major (equatorial) axis and a minor (polar) axis. 



The planetary variation in the gradient may be obtained by differentia- 

 tion of formula (7-156), disregarding the longitude term so that the plan- 

 etary gradient is 



dg _ dg^ 

 pxdip Rdcp 



(t/„) 



iz/norm. 



\dX/n 



(7- 63) 



where px is the radius of curvature of the meridional ellipse, which in this 

 case is sufficiently close to the earth's radius so that after substitution of 

 the numerical values from eq. (7-156) 



(7-64) 



(t/xz)r 



= 8.16-10" -sin 2^. 



The variation of gravity and gravity gradient with latitude is shown in 

 Fig. 7-73a. It is seen that the north gradient is zero at the equator and 

 the poles, is always directed toward the north or south pole, and has a 

 maximum at 45° latitude. Under the conditions assumed (two-axial 

 ellipsoid of revolution), there is no variation of gravity along the parallels 

 of latitude, and hence no correction need be appHed for planetary variation 

 to the observed values of Uy^. If the instrument is oriented into the 



