MAGNETIC METHODS 



185 



tial. The potential at any point due to a magnetic pole of strength m may 

 be defined as the work done in carrying a unit pole from infinity to the 

 point in question. That is, the potential f" may be defined by the equation : 



(67) 



Fig. 75.— Field at P due to S pole of 

 strength m located at a depth d. 



The components of the magnetic field (Figure 75) at a point (x, y) due to 

 a pole of strength m located at a depth d are : 



AX=:- 



dV_ 

 dx 



mx 

 my 



dy r 



AZ = - 





md 



(68) 



The horizontal component of the field due to the pole m is : 



dV 1HU 

 ou r"^ 



(69) 



The actual shape of the curve obtained on plotting AH or AZ depends 

 on the depth to the top of the ore body and the pole strength. Figure 76 

 shows the profiles in the ^'-direction (3; = 0) when d = —1 and m = —2. 

 For this case, Equations 68 and 69 for the vertical and horizontal intensity 

 anomalies become 



'''"^ 2 (68a) 



_ md 



{d'^ + x'^y^ (l+.t-2)% 



