Chap. 10] 



ELECTRICAL METHODS 



673 



This expression is zero when x is zero, so that, from (10-196), 



2h^ ' 



V = 



' max. 



(10-19d) 



An approximate calculation of the depth of the doublet may be made by 

 determining the distance of the "half-value" point of the curve from the 

 point of the maximum. Equating the general expression for the potential 

 in (10-196) to one-half the maximum value given by (10-19d), we get 

 (x?/2 + hY^ = 2h\ which gives 



a;i/2 



= h V^ - 1 = 0.7Q7h. 



(10-19e) 



The expression in eq. (10-19c) signifies current density. An analysis of 

 the curve representing the variation of this quantity with distance is 



Fig. i0-24a. Potential curves for polarized spheres of various angles of inclination 



(depth h = 2). 



useful for depth determinations as follows: Differentiating (10-1 9c) again 

 with respect to x and equating the result to zero, we find that a maximum 

 occurs when 



= ± h/2. 



(10-19/) 



It follows from (10-19c) and (10-19/) that the current density above 

 the vertically polarized sphere is zero and that on either side a maximum 

 and minimum occur whose distance is equal to the depth to the center 

 of the sphere (see Fig. 10-246). It should be recalled that current density 

 and therefore potential gradient is obtainable directly in the field from 

 voltage readings with constant electrode separation. 



A dipping ore body may be considered equivalent to a polarized sphere 

 whose axis of polarization makes an angle a with the vertical. Resolving 

 this inclined doublet into two doublets of the respective moments m cos a 



