Chap. 7] 



GRAVITATIONAL METHODS 



227 



terrain profiles. For this purpose diagrams are used which contain the 

 outUnes of mass sectors of such dimensions that their effect on the instru- 

 ment is identical regardless of distance or azimuth. Hence, the determina- 

 tion of terrain effects is accomplished by "counting" the number of "grati- 

 cule" elements encompassed by the successive contours or the terrain 

 profile. In the first case we speak of "horizontal" diagrams; in the second, 

 of vertical diagrams. The construction and use of horizontal diagrams is 

 based on the calculation of sector plans of such dimensions that for equal 



Fig. 7-77. Cartograpliic correction with contour lines. 



elevation their effect on the instrument is equal. An approximation 

 method (Numerov^^) and a rigorous method (K. Jung^*") have been de- 

 veloped. 



Numerov's method of calculating terrain diagrams rests on eq. (7-69), 

 which, for an element bounded by successive radii Pn and p^+i and angles 

 am and am+i, may be written in the following form, provided f is negligible 

 compared with p^ in the denominator: 



"'Zeit. Geophys., 4(3), 129 (1928). 

 >««Zeit. Geophys., 3(5), 201 (1927). 



