214 



GRAVITATIONAL METHODS 



[Chap. 7 



graphical, and (c) integraph methods. In the first, elevations measured 

 in the field in predetermined azimuths and radii about the instrument are 

 substituted in formulas with fixed coefficients for such azimuths and dis- 

 tances. In the second method, evaluation diagrams, or "graticules," are 

 used which are superimposed upon a terrain contour map or upon terrain 

 sections in predetermined azimuths. A count is made of the number of 

 diagram "elements" which are included within adjacent contour lines, or 

 between the terrain profile and a plane through the center of gravity of the 

 balance beam. In the integraph methods, contour maps or terrain profiles 

 are evaluated directly by specially constructed integraphs. 



Terrain correction methods are numerous, and only those differing 

 sufficiently in mathematical principles or procedure will be discussed. 



Fig. 7-74. Mass element in relation to center of gravity of torsion balance. 



Their description will proceed in the order given above and will be con- 

 cluded with a discussion of application and field practice. 



(a) Analytical methods. The fundamental principle underlying not 

 only the analytical but all other terrain-correction methods is to divide 

 the surrounding terrain into sectors bounded by angles and concentric 

 circles and to sum up their effects. The action of each sector is calculated 

 in the analytical methods by assuming definite variations from one azimuth 

 to another and from one circle to another. Within two successive circles 

 all sectors have the same opening. (In the graphical methods the sectors 

 are all different and so calculated in respect to azimuth and distance that 

 they exert the same effect on the instrument.) 



The action of each sector follows from the effect of a mass element dm 

 (see Fig. 7-74). Since its gravity potential at the distance r is U = 



