392 



MAGNETIC METHOD 



[Chap. 8 



which, when, differentiated with respect to x and d, give the horizontal 

 and vertical intensity anomalies due to each magnet: 



and 



AX, 



AX. 



37, 

 bx 



dx 



dd 



M. 



+ 



ZMz'X-d 

 dM^'X-d 



> (8-58e) 



dd r r^ 



By addition of the partial components, the anomalies become 



AH = -AK'.-j3Zorc6^ - Ho(2a:' - d')] 

 AZ = -A/c'.-j3HoX(^ + Zo(a;' - 2d')], 



(8-58/) 



where v, as before, = iirR^ and A/c' is given by eq. (8-58c). Although 

 spherical bodies are rarely encountered in nature, analysis of this case 

 has the advantage of demonstrating clearly how the magnetic effects of 

 geologic bodies depend on the magnetic latitude (see Fig. 8-51). 



For an infinite cylinder the magnetic effects can be cast in simple form 

 when the section S of the cylinder is in the plane of the magnetization, 

 that is, if strike magnetization of the cylinder is zero. Then, according 

 to Haalck:^^ 



and 



AH = -2bK' --nZoxd - Ho(a;' - d')] 



AZ = -2Ak'.- r2Hoxd + Zo(a;' - d^)]. 



) (8-59) 



These relations, as is to be expected, are similar to those for the sphere 

 (eq. 8-58/). 



Griesser and Koenigsberger have calculated the magnetic anomalies in 

 vertical intensity, horizontal intensity, and declination, for ellipsoids of 



*^ Die magnetischen Verfahren, op. cit., p. 54. 



88 J. Koenigsberger, Gerl. Beitr., 19(2), 241-291 (1928). 



