Chap. 8] MAGNETIC METHOD 389 



9. With line-of-force diagrams, depth, dip, and approximate dimensions 

 of ore bodies can be determined from anomalies represented by vectors. 

 The method is applicable to bodies whose effect may be approximated by 

 bar magnets and magnetized plates. Since the vectors are tangent to the 

 lines of force, the diagram is applied by placing the equivalent magnet in 

 such a position beneath the surface that its force-line distribution satisfies 

 the arrangement of the vectors measured at the surface. The con- 

 struction of force-line diagrams proceeds in accordance with the relation 

 cos a — cos /3 = n = constant, where a and ^ are the angles between the 

 axis of a magnet and lines drawn from any point on a line of force (given by 

 the constant n) to the north and south pole of the magnet. The diagram 

 shown in Fig. 8-49 may be adapted to equivalent magnets of different 

 lengths by photostatic reduction or enlargement. 



D. Induction Theory 



The pole and line theory discussed above makes no assumption regarding 

 the origin of the poles or pole series in a magnetized body. It is valid for 

 any strength and direction of magnetization, regardless of origin. On the 

 other hand, certain types of geologic bodies (some iron ores, igneous rocks 

 of medium susceptibility, and magnetic sedimentary rocks) show mag- 

 netic anomalies which are obviously related to the strength and direction 

 of the earth's magnetic field. In such cases it is advantageous to apply 

 an interpretation theory which expresses the magnetic anomalies as a 

 function of susceptibility, dimensions, and disposition of geologic bodies 

 and as a function of the strength and direction of the earth's field. Un- 

 fortunately, the "induction theory" is handicapped by the fact that the 

 field produced by many types of geologic bodies cannot be calculated 

 accurately, since even bodies of uniform physical composition are not 

 uniformly magnetized except when bounded by second order surfaces. In- 

 vestigators have, therefore, sought a way out of the difficulty by one of 

 two courses: (1) by approximating the shape of geologic bodies by spheres, 

 infinite cylinders, and ellipsoids of revolution; (2) by dropping the premise 

 of uniform magnetization and calculating the effects of actual bodies as if 

 they were uniformly magnetized, that is, by disregarding the effects of 

 flux concentration on edges and corners. ^^ The literature dealing with 

 both phases of the induction theory is fairly extensive ; the more important 

 articles are enumerated below: 



1. Eotvos, R. v., 15, Allg. Conf. Int.Erdm., 392-394 (Budapest, 1906). 



2. Winkelmann, A., Handb. d. Phys., 5, 140 (1908). 



" This fundamental limitation of the theory is often overlooked in articles dealing 

 with this phase of the induction theory. 



