Chap. 7] GRAVITATIONAL METHODS 153 



Adding to this the effect of a vertical step (7-42(i), the following gravity 

 anomaly for a slope (Fig. 7-44e) is obtained : 



A^ = 2k8< — [x sin i -{- d cos i] sin i loge — + cos i((p2 — <pi) 



+ D^i - d<pi\. (7-43fe) 



Above a very extended slope, Vz/n = 1, ^2 — <pi — t, c?^i — and 

 cos * ^ 1 so that 



A^ = 2k8 i-kix sin i -{• d) -{- D^z] (7-43c) 



By a subtraction of two slopes with identical dip, the effect of an inclined 

 bed, ore vein, or the like (Fig. 7-44/), can be calculated: 



= — [x sin i -\- d cos i] sin i loge -^ + cos i{(p2 — <pi + (P3 — <fi) 



L nn J 



+ 6 sin i sin i loge - + cos i(v4 — y's) + Di(p2 — (Pi) — d((pi — (ps). 

 L rs J 



(7-43rf) 



If the inclined formation has great depth, the same approximations as 

 before may be introduced, namely, rz = n and D((p2 — (Pi) = h, so that 



2k8 



Ag 

 2k8 



= — [x sin i -\- d cos i] sin z loge — + cos i((p2 — v^i + ^3 — f*) 



•[• 



r4 



+ 6 sin i sin i loge - + cos i((pi — v^s) + 6 — d((pi — (ps). 

 n J 



(7-43e) 



For symmetrical anticlines and synclines (Fig. 7-44^ and h) the anoma- 

 lies are calculated by adding the attractions of two triangular prisms or 

 slopes respectively. 



3. In graphical interpretation methods, graticule diagrams are super- 

 imposed on structural maps or profiles. Gravity anomalies are obtained 

 by counting the mass elements included within adjacent contours (three- 

 dimensional diagrams), or (in profiles) within the outlines of the forma- 

 tions involved (two-dimensional diagrams). Construction of the former 

 is based on the same analysis that is used in the preparation of terrain 

 correction charts (see page 138) or the calculation of the effects of cylindrical 

 compartments (see page 149). In application the scale of the geologic 

 sections must be considered. The calculation of two-dimensional dia- 

 grams is based on formula (7-39/) with polar coordinates. A vertical 



