582 EXPLORATION GEOPHYSICS 



An inspection of the figure shows that sin 6 = cos /?. Hence, 



jzT — ^ ^^ cos /? 

 ari — 5 



If X is the perpendicular distance from the point P to the conductor I, 



r = jf sec y8 

 1= X tan p 

 dl= X sec2y8 d/3 

 Substitution of these values of r and dl into the expression for dH yields 



, „ _ I X sec^ ^ dp cosyS 



^-" ~~ 2 2o 



x^ sec'P 



and 



rr_. \ / COS ;3 dff 

 /0, 



On carrying out the integration, one obtains 



H= -(sin;32-sin;8i) (2) 



If the wire is very long compared to x, /?2 approaches + ir/2 and /?i ap- 

 proaches — 7r/2. Equation 2 approaches the familiar form for the field 

 about an infinite wire: namely, 



27 

 H=— (2a) 



X 



Equation 2a shows that the field surrounding a linear conductor may be 

 represented by concentric circles, as was illustrated in Figure 361. 



Conductive Methods 



Magnetic Field Produced at the Earth's Surface by Subsurface 

 Current. — When current is conductively supplied to the earth a mag- 

 netic field will be set up, and a portion of the field will exist at the surface 

 of the earth. Since the current distribution in the earth will be influenced 

 by the geologic structure, the magnetic field set up by the current will like- 

 wise be influenced and measurements of this magnetic field or quantities 

 which depend on this field give an indication of the subsurface geology. 



For a given electrode spacing the greatest flow of current is along 

 the path of greatest effective conductivity. As applied to mineral pros- 

 pecting, the effective conductivity of a sulphide zone is much greater than 

 that of the surrounding medium, and the mineralized zone may therefore 

 be located by studying the magnetic field at the surface of the ground 

 and by finding the path along which the current flow is greater. When 



