156 



GRAVITATIONAL METHODS 



[Chap. 7 



into a surface integral independent of distance and azimuth by the 

 substitution^ = \/2rand$ = cosv?. Then / I sin <pd<pdr = \ I I RdRd^. 

 The resulting scale distortion may be seen in Fig. 7-47. 



10 9876543Z 7 S725456789 10 



Fig. 7-47. Radial and vertical angle scale distortion for planimetric determinations 

 of anomalies of two-dimensional masses (after Jung). 



Scale distortion may be avoided by the use of a special integraph. If 

 the double integral in eq. (7-39/) is reduced to a single integral, the at- 

 traction of a two-dimensional body may be written 



A^ = 2kb I r sin (f d<p. 



(7-44c) 



The function of the integraph shown in Fig. 7-48 is to carry out the 

 multiplication d<p X r sin tp. It cojisists of a finder, F, moving radiall}^ 

 (distance r) on the arm, A, which in turn is rigidly coupled to the disk, 

 D. The latter thus rotates by amounts d<p when a section is traced. The 

 finder, F, engages the bridge, B, which carries the roller, R. This roller 

 is rotated by the disk, D, and transfers its reading to the scale, S. Be- 

 cause of the coupling of A and B, the distance of the roller from the 

 center (station) is thus always r sin <p and is rotated by the amount of this 



