Chap. 10] ELECTRICAL METHODS 767 



X component is zero and the other components are given by Y = T sin v5 

 and Z = T cos «p. Since cos «p = y/r and sin (p = d/r, we have 



Y = 



2rd 27'd 



2/2 + rf2 



and 



r^ y^ -\- d^ 



> (10-46a) 



Since dY/dy = ii y = 0; dZ/dy = for y = ztd,Z = if y ^ and 

 a'Z/dy^ = for ?/ = 0. 



The horizontal component has a maximum directly over the current con- 

 centration (y = 0) and the maximum intensity is Ymax. = 21' /d. The 

 maximum gradient in vertical intensity is directly over the ore body where 

 the vertical intensity itself is zero. A maximum in vertical intensity 

 occurs on either side at a distance from the zero point equal to the depth. 

 The distance between the maximum and minimum vertical intensity 

 anomalies is therefore equal to 2d. For an ore body of definite width and 

 infinite depth extent which can no longer be considered equivalent to a 

 current concentration (see Fig. 10-92c), 



Z = 27Moge-' 

 Y = 21' (<p2 ± ^i)- 



> (10-466) 



Curves for bodies of various dimensions, dip, and depths have been 

 published by Mueller. " Heine has calculated the electromagnetic field for 

 rectangular sections of various dimensions, at right angles to the direction 

 of current flow.^^ He assumed that the current density throughout the 

 section was uniform which is permissible within the conductor itself. It 

 is necessary, however, to allow also for the decrease of current density 

 with depth, which was previously discussed (see Fig. 10-32 and eq. 

 [10-21e]). 



Belluigi has compiled a set of curves, showing the variation of current 

 in the median plane between two electrodes as a function of base length.^ 

 When the current density for a given depth has been found, the electro- 

 magnetic field components may be determined^^ for a conductive bodj'^ of 



"GerL Beitr., 21(23), 249-261 (1929). 



'3 W. Heine, Elektrische Bodenforschung, 137, Borntrager (Berlin, 1928). 



«*A. Belluigi, Beitr. angew. Geophys., 1(4), 370 (1931). 



85 Ibid. 



