Chap. 7] 



GRAVITATIONAL METHODS 



155 



an ordinary planimeter (Below's method^^). According to eq. (7-38c), the 

 anomaly produced by an element r dr dip, whose elevation appears at the 



angle yp, is given by ^g = — A;5(l — cos i/')- / / dr-d^p. If a new radius, 



R, is substituted for \/2r, the anomaly becomes 



A(/ = - \kb{l - cos yp) If R dR dip, (7-446) 



where R dR dip is an 

 areal element whose 

 attraction now is in- 

 dependent of distance 

 and requires repre- 

 sentation in a scale so 

 distorted that R = 

 1.4 Vr (Fig. 7-46). 

 If the surface eleva- 

 tions are represented 

 by Unes of equal angle, 

 ^, terrain effects be- 

 tween adjacent con- 

 tour lines may be 

 determined by plani- 

 metering. The same 

 method is adaptable 

 to calculation of irreg- 

 ular subsurface masses 

 represented by con- 

 tours. For two-di- 

 mensional features it 

 is necessary to distort 

 both the radius and 

 the angle scale. In 

 formula (7-39/) the 



integral / / sirup dip dr 



may be transformed 



I-^X 



*' K. Jung, o-p. 

 6(2), 114-122 (1930). 



cil., 



Fig. 7-46. Radial scale distortion for planimetric 

 determinations of attractions due to three-dimensional 

 masses (after Jung). 



