GRAVITATIONAL METHODS 



335 



4bn = — ^ (22 — ^6 + -4 - -^s) + 53 



Zl 



4Cn = —= (So - 2q-Z^ + Ss) +S1-25 

 4dn = ^2—^4+^6 -28 



4en= 2i 



+ 2r 



(96) 



Schweydar now makes the assumption that the variations in height 

 from one circle to the next in any given azimuth are proportional to the 

 radial distances from the station. The values of the integral expressions 



'^2 T T o2 T T 



, etc., obtained on this assumption are as follows : 



for 



?)x'ds ?)y'd2 





= (KiCi + K2C2 + 



^ = (K^b, +K2b2 + 



dyd2 



'd-'^'dy 



= — (LiCi + Lo^o + 



(97) 



where Ci, bi, di, ei, refer to the first circle, Co, bo, . . . etc., refer to the 

 second circle, and so on, and the i^'s and L's are constants which depend 

 only on the values of h and the values of the successive radii. 



Schweydar computed the terrain efifects for h equal to 90 centimeters. 

 In his second paperf he gives a more rigorous treatment for the evaluation 

 of terrain effects without neglecting the 2^ term. 



For the evaluation of cartographic effects, contour lines based on reason- 

 ably detailed general topographic surveys are used chiefly. There are other 

 methods, however, which are sometimes applied for the evaluation both of 

 terrain and -cartographic corrections. 



Numerov,* for example, devised a convenient graphical method for 

 the determination of gradients due to topographical features by assuming 

 that the value of r is large (over ZZ meters) and by computing the 

 effect due to a prism of mean height Zi, the cross section of which is in- 

 cluded between radii r„ and r„ + i which are in azimuths Qm and Qm + i. 

 The principle of this method is to divide the area surrounding the station 



into zones such that the quantity I -—5 — I (cos Q^n — cos Q,„) is 



\Zr„ Zr„ + i / 



constant. The application of the method is described by Broughton Edge 



and Laby. {loc. cit.) 



t W. Schweydar, Zeit fiir Geophvsik, Vol. 2, pp. 17-23 (1927). 



tB. Numerov, Zeit fur Geophysik. Vol. 1, pp. 367-371 (1925); Vol. 4, pp. 117-134 (1928). 



