Chap. 7] 



GRAVITATIONAL METHODS 



149 



and 27r, we obtain, for a cylindrical 

 sector (Fig. 7-42a) with the central 

 angle <p, 



A^ = ^U\l - {ji - r-u)]; (7-41a) 

 and, if the station is on the sector, 



Ag = ipkhW - (r, - p)]. (7-416) 



For a cylindrical compartment the 

 gravity anomaly with notation as 

 used in Fig. (7-426) is 



A^ = ip}:h{rz -\- Ti — r^ — r^, (7-41c) 



which follows from (7-41a) by subtraction of an inner from an outer 

 sector. 



Eq. (7-41c) has a wide application, since irregular three-dimensional 

 masses may be divided up into such compartments. It may, therefore, 

 be used for terrain corrections. Substituting for 



Fig. 7-42. Cylindrical sectors and 

 segments. 



n : Vp5 + ct n : Vp? + (d + Xf 



rt : Vp^ ^ct u: Vpl + (d + 0', 



and letting d = and I = h, since the station is usually located level with 

 the lower surface of the segment, 



A^ = ,pk8(pi + Vpl + h' - Vpf+T^ - p2), 



which is identical with (7-38a). 



Formula (7-41c) may also be used for computing the effect of irregular 

 subterranean masses. In practice, however, formula (7-40d) is preferred 

 in the form 



Ag = 27rfc5(VpHM' - V7TT+W + ^)> 



which may be written 



(7-41d) 



In this equation d/p and l/p are considered as variables^ (see Fig. 

 7-43). To find the anomaly of a sector, the effect of a cylinder of given 

 l/p and d/p ratio is obtained from the graph and multiplied by the outer 

 radius, ps. From it the effect of another cylinder is subtracted (likewise 



" See F. E. Wright and F. A. Vening Meinesz, Bull. Naval Obs., XIII, app. 1 

 (1930). 



