148 GRAVITATIONAL METHODS [Chap. 7 



1 37). It is significant that in formula (7-40e) no effect of depth is contained. 

 The gravity method has, therefore, no resolving power; for very extended 

 formations their attraction is proportional to thickness but not to depth. 

 It should be noted at this point that in all equations concerned with 

 gravity anomalies of heavy bodies, the difference between the density of 

 a body, 5', and that of the surrounding formation, 5o, must be substituted 

 in place of the absolute density, so that 



5 = 5' - 6o. (7-40/) 



A few other extremes of formula (7-40rf) are of interest. If a station is 

 located on the upper surface of a cylindrical mass, the anomalous gravity 

 is, 



Agf = 2irkb[l - (ri - p)]. 



If the cylinder is very long compared with its radius, the gravity anomaly 

 is 



A^ = 2Tk8p. 



This indicates that for a very long cylinder the gravity effect depends 

 only on its radius. In Special Publication No. 99 of the U. S. Coast and 

 Geodetic Survey, tabulations are given for the effects of cylinders of vary- 

 ing lengths (or depths to bottom), I, and varying radii, p, for a station 

 located at the center of the upper surface. 



These tables may also be used (1) if the station is not located on the 

 upper surface, but at a distance, d, above it; (2) if the station is located 

 off the cylinder, but in the level of the upper surface; (3) if the station is 

 both off the center and above the upper surface of the cylinder. In the 

 first case the attraction of a second cylinder with h = dis subtracted from 

 that of a cylinder of the length li. In the second case, if the distance 

 between station and axis of the cylinder is R, anomalies of two cylinders 

 are subtracted from each other. Thus, the effect of a hollow cylinder is 

 obtained, whose thickness is equal to the diameter 2p of the cylinder 

 wanted. Its effect is then multiplied by the ratio of the surfaces, (sought 

 cylinder) /(surface ring), so that in abbreviated notation 



where C(R+p) is the attraction of the cylinder with the radius R -\- p, and 

 C(R-p) is the attraction of the cylinder with the radius R — p. If the 

 station is off center and above the cylinder, the procedures followed in the 

 first and second cases are combined. 



From eq. {7-AOd) and by integrating between and <p instead of between 



