768 



ELECTRICAL METHODS 



[Chap. 10 



arbitrary section by the use of gratings similar to those applied in gravi- 

 metric interpretation (see page 154). Since the magnetic field is propor- 

 tional to the section of an element in which the current density is uniform, 

 the field components are, for an element dydz traversed by a current in 

 the X direction : 



Y = 



'^^ li y^ 



y^ + z' 



dydz 



y"^ + z' 



dydz. 



(10-47a) 



Substituting y — ^ cos 5, 2 = R sin ^, and dydz = R-d6dR, we have 

 for the same components 



Y = -21' J j sin Odd dR 



= --'ll 



cos Odd dR. 



(10-476) 



Fig. 10-90. Subsurface element traversed by current between two electrodes. 

 Hence, for a plane element, as in Fig. 10-90, the intensities are given by 



Yik = -21' sin Odd / 



and 



-21' / cosdde / 



[ (10-47c) 



Zj.ii 



'Rk+i 

 cos Odd I dR. 

 'Rk 



The fields of all elements in the section are therefore 



Y = Z 2/' (cos ^i+i - cos ^i)(Rk+i - Rk) 

 Z = ^ -21' (sin ^i+i - sin 0i)(Rk+i - Rk). 



(I0^7d) 



