Chaf. 8] 



MAGNETIC METHOD 



381 



The induction theory is based upon a relation between the gravitational 

 and the magnetic potential of a body, provided that it is homogeneously 

 magnetized. Since this holds only for bodies bounded by second order 

 surfaces (spheres, ellipsoids of rotation, and the like) which do not occur 

 in nature, the application of the theory to actual forms of geologic bodies 

 (plates, slabs, and so on) results in approximate data only. For these 

 reasons the simpler pole and line theory has been widely used (since about 

 1870), particularly in magnetic mine exploration. Ore bodies may be con- 

 sidered magnetic poles, doublets, or single and double magnetized lines. 

 Irregular masses, such as igneous intrusions, granite ridges, and the like, 

 can be treated as pole series. The pole theory can be applied regardless 

 of whether magnetic effects are due to induction or any other cause, as 

 long as the positions of the poles are known. 



C. Pole and Line Theory 



1 . Single pole, depth rules. Ore bodies may be re- 

 presented by single poles if they occur in the form 

 of pipes, chimneys, and the like, if their section is 

 lenticular or circular, and if they are small compared 

 with their depth extent so that the lower pole may be 

 assumed to be far away from the upper. The as- 

 sumption of a single pole is justified if the isanomalic 

 lines of the vertical intensity are nearly circles or short ellipses, and if 

 only a positive anomaly exists. Assume (Fig. 8-44) a pole^' of strength m 

 at depth d below the surface. The magnetic potential of the pole at 

 P{x, y, dy^'^ is F = m/r, and the force in the direction of r is F = dV/dr = 

 — m/r^. Hence, its components: 



Fig. 8-44. Single 

 pole. 



(8-52a) 



*' Contrary to the conventional designation, the South Pole is here positive, so 

 that the vertical intensity anomaly is positive. 



83" The X is positive toward north (away from m);y is positive toward east (like- 

 wise away from m); but d is positive downward {toward m, from surface). 



