Chap. 7] GRAVITATIONAL METHODS 147 



tance R from the axis and a distance e from the point P at the surface so 

 ^hat 



dm = b-dl-Rda-dR. 

 According to eq. (7-396), its potential at P is 



which gives, for a circular disk of thickness AZ and radius p, 



U = 2wk8Mi\/d^ + p2 _ d). 

 Hence, the gravity anomaly 



A^ = -^ = 27rA;5AZ (1 - -,- ). (7-406) 



dd \ y/d^ + p^) 



With notation of Fig. 7-41 : 



Ag = 2TtkbM M - - j = 27rA;5AZ(l - cos 6). (7-40c) 



By additional integration, the potential of the entire cylinder is 



,2. ,d+i rp^^dindji 



U 



Jo Jd Jo 



'0 Jd Jo C 



and, therefore, its attraction, from eq. (7-406), is 



^g = 2tU I dl ( i - - J- y 



which gives 



A(7 = 27rA;5[/ + VdMh"7' - VpH- {I + li?] 



and with notation as in Fig. 7-41 



^g = 27rA;5[Z - {n - r„)]. (7-40d) 



Equations (7-40c) and (7-40d) permit a number of interesting deductions 

 for extreme cases. 



If the radius of a thin disk becomes very large, cos d is zero. Therefore 

 the gravity anomaly due to an infinite bed of thickness Ai, is 



Afir = 2irkbM. (7-40e) 



This formula is identical with that giving the attraction of the rock 

 material between station and sea level in Bouguer's reduction (see page 



