GRAVITATIONAL METHODS 257 



calculatable shape. The most convenient shape mathematically is a flat 

 cylinder or disc of material (similar to a large grindstone) as illustrated 

 in Figure 125. The gravity station is assumed to be located at the center 

 of the top surface of the cylinder. The height H of the cylinder is small 

 in comparison to its radius. The radius may be considered as infinite, so 

 that the correction takes into consideration all the material from the station 

 elevation to datum. 



According to Helmertf the attraction of a mass of this shape on a 1 

 gram mass at the station location is : 



A^ = ZttG d-H (17) 



wherein Ag = the gravity effect of the cylindrical mass; G = the gravita- 

 tional constant; d = the density of the material in the cylinder, and H = 

 the height of the station above the datum or thickness of the cylinder. 



As previously given in Equation 5, the attraction of the earth on the 

 same unit gram at the station is : 



g = GM' 1/R' = G 4/37rR' a/R' = G A/SnRo- (5) 



(In the above M and R are the mass and the radius of the earth, respectively, 

 and a is its mean density. G is the gravitational constant.) 



Dividing Equation 17 by Equation 5 and solving for Ag gives : 



Ag ZttG d H , ^ ,^ d H ,.„- 



g= G4/i,R. -^S = gi/2--^ (18) 



This correction amounts to 0.04185 dH milligals per meter, or 0.0127 

 dH milligals per foot. 



Application of Corrections. — The elevation correction and the Bou- 

 guer correction are of opposite algebraic sign. They are usually combined 

 for convenience, and applied to observed gravity values, together w^ith a 

 terrain correction, which latter will be considered in the section on gravi- 

 meters. (See p. 404.) After correcting for elevation, Bouguer effect and 

 (if necessary) for variations in terrain around the station, the gravity 

 values are given the symbol g"o and are generally called Bouguer gravities. 



A gravity value as measured at any given station can be reduced to the 

 datum by making the elevation correction. This corrected value is the one 

 which would have been obtained if the original reading had been made at 

 the datum.* It represents the observed value of gravity plus the elevation 

 effect, but does not consider the column of material between the datum and 

 the surface. 



t Helmert, loc. cit. 



* Gravity at datum is greater than at the ground surface (when datum is below 

 the station, as is generally the case). Gravity at a point nearer the center of the earth 

 (datum) is greater (less R distance, Equation 5) than at the surface. The elevation 

 correction is therefore plus and is added to the observed gravity. 



