Chap. 10] 



ELECTRICAL METHODS 



787 



(page 687) it was shown that elliptical polarization results from a combina- 

 tion of two vectors which differ in coordinate and phase. The combina- 

 tion of two vectors that differ in direction and are in quadrature, likewise 

 results in elliptical polarization. This combination applies in electromag- 

 netic methods. As illustrated in Fig. 10-108, a horizontal loop laid on the 

 ground surface induces a current to flow in opposite direction along the 

 upper edge of an ore body whose magnetic field at the distance r from the 

 current concentration is given by the vector T. This vector combines 

 with the vertical loop field Zo and is in approximate quadrature with it. 

 The components of T are: Y = T cos 6, and Z = T sin 6. The difference 



Fig. 10-108. Composition of loop field and eddy current field. 



in the vertical components is Zi = Zo — Z. If all vectors oscillate with 

 the same frequency and T = B cos ut is in quadrature with Zo = A sin o}t, 

 then 



and 



Zi = A sin 0)1 — B cos ut sin 6 



Y = B cos cot cos 6. 



> (10-536) 



Since, in the second equation, sin o)t = v 1 — cos^ wt = =i , 



B cos 



the first equation becomes, by substitution, ZiB cos 6 -j- BY sin 6 = 



