MAGNETIC METHODS 



205 



The total x component ^.H due to M^ and Mg is 



AH = (AH)^ + (AH), - —^^ -^ ^^ (97) 



and the total s component AZ due to Ma, and Mg is 



A7-rA7^ -^rA7^ _ ^M,xd M,x^ 2MJ^ 



AZ= (AZ)^+(AZ),- ^s +-^ ^:^— (98) 



Equations 97 and 98 may be simplified by expressing the magnetic 

 moments M^ and M^ in terms of the horizontal and vertical components H 

 and Z of the earth's normal field. That is, 



M^=cH = cZ^ 



and 



Mg = cZ = cH 



Z_ 



H 



On substituting these values into Equations 97 and 98 and simplifying, 

 one obtains t 



AH = -^ (2x^ -d^- Sxd ^ \ (99) 



1=14/2° 



1=45- 



1 = 65' 



Pig 97. — Sketches illustrating the anomalies produced by a uniformly magnetized sphere in regions 

 of different inclination. (After Haalck, Die Magnetischen Verfahren der Angewandten Geophysik.) 



Equations 99 and 100 show that the anomalies AH and AZ depend on 

 the normal values H and Z. That is, the anomalies produced by a uni- 

 formly magnetized sphere depend on the normal value of the inclination 

 of the earth's field in the region in which the subsurface sphere is located. 

 The AH and AZ profiles for three values of the inclination are shown in 

 Figure 97.$ 



t Compare H. Haalck, "Die Magnetischen Methoden der Angewandten Geophysik," pp. 330-332. 

 Handbuch der Experimentalphysik, edited by W. Wien and F. Harms. (Akademische Verlagsgesell- 

 schaft M.B.H., Leipzig 1930.) Vol. 25, part III. 



t H. Haalck, Die Magnetischen Verfahren der Angewandten Geophysik (Gebruder Borntrager, 

 Berlin, 1927). 



