390 MAGNETIC METHOD [Chap. 8 



3. Carlheim-Gyllenskiold, V., Magnetic Survey of Kiirunavaaia (Stock- 

 holm, 1910). 



4. Griesser, R., Diss. Freiburg (1921). 



5. Steiner, L., Terr. Mag., 26, 81 (1921). 



6. Haalck, H., Zeit. Geophys., 2, 1-11 and 49-62 (1926), 4, 267 (1928); 

 Gerl. Beitr., 22, ?41-255 and 385-399 (1929); Handb. Exper. Phys., 

 26(3), 320-347 (1930); Die magnetischen Verfahren, etc. (Berlin, 1927). 



7. Bahurin, J., Inst. Pract. Geophys. Bull., 2, 3 (1926); 3, 255 (1927); 

 4, 3-78 (1928). 



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



9. Gamburzeff, G. A., Gerl. Beitr., 19(2/3), 210-230 (1928). 



1. Fields of uniformly magnetized bodies (spheres, infinite cylinders, ellip- 

 soids of revolution). In Fig. 8-50a let P be a point of observation with 

 the coordinates x and d in the plane of magnetization of a small sphere of 

 susceptibility k and volume v. The potential V of the doublet with the 

 poles -f-m and — m produced by the earth's field is equal to the sum of the 

 potentials due to each pole. Thus V = m/ri — m/rj = m(r2 — ri)/ri-r2 . 

 By substituting r^ for ri-n, cos <p for (vi — ri)/2R, and M (magnetic 

 moment) for 2Rm, the potential 



Since the magnetic moment is the product of intensity of magnetization 

 3 = kTo (To = total intensity) and volume v = i irR^, its components due 

 to magnetization by the horizontal and vertical intensities (see Fig. 8-50a) 



M^ = i t^'kHo and M, = i wR\Zo . (8-586) 



This induced magnetization is accompanied by a demagnetization effect; 

 the opposing field, H', is proportional to the intensity of magnetization 

 B, or H' = N^, where N is the demagnetization factor. The resultant 

 magnetization is therefore B = k(To + H'), or ^ = kTo/(1 + Nk). For 

 the sphere the demagnetizing factor N = 47r/3 and the total intensity 

 T = To -h H' = To- 1/(1 + |ir/c). Therefore, the resultant intensity of 

 magnetization is ^ = To/(l -|- iirK). If the sphere is imbedded in a 

 medium of the susceptibility kq and if Ak = k — ko , ^ = AkTo/(1 + f7rA/c). 

 Designating the factor Ak/(1 + ^ttAk) as k', the magnetization 



B = Tq.Ak '. (8-58c) 



The demagnetizing effect results therefore in reduction of the true to 

 an apparent susceptibility. It is negUgible for bodies of low suscepti- 

 bility. For strongly magnetic bodies, such as magnetite deposits, it may 

 result in an appreciable decrease in susceptibility. 



