692 ELECTRICAL METHODS [Chap. 10 



Since the inclination of the tangent to the elUpse is given by tan (90 — a) = 



1,2 



X 



— — , we have 

 a* y 



(3) tana = |.|. 



Dividing eq. (2) by eq. (1) and substituting in (3), we obtain the following 

 relation between the azimuth of the line and phase angle 



tan a = J. tan 5. (10-266) 







If we substitute eq. (10-266) in eq. (10-26a), the amplitude in the line OA 

 as a function of phase angle and ellipse axes is 



1^1' = r2 — 2/T2 • 2, • (10-26C) 



6^ cos^ 5 + o^ sm^ 8 



In the mapping of the A.C. ground-potential distribution, it is not 

 customary to survey the ellipse and deduce the ratio of major and minor 

 axes and ratio of in-phase and out-of-phase field components, as is done in 

 the determination of propagation characteristics of radio waves. When 

 elliptical polarization is noticeable, potentials are generally determined 

 with a compensator which measures their amplitude and phase with ref- 

 erence to those of the primary supply"; or else the in-phase and quadrature 

 potentials are determined, and equipotential lines are drawn separately 

 for each. These procedures are discussed in the following section. 



C. Field Procedure; Equipment 



Direct or alternating current may be used for surveying equipotential 

 lines. Direct current has the advantage that the equipotential points can 

 be located with greater precision and that the galvanometer gives a clear 

 indication of the direction in which , to move the electrode. A disad- 

 vantage is the necessity for porous pots and the interference from polariza- 

 tion and other D.C. effects. Alternating current has the advantage of 

 portability and convenience of the movable circuit, possibility of amplifica- 

 tion of signals, and freedom from commercial current interference. Dis- 

 advantages may arise from its use in highly conductive regions because 

 out-of-phase components prevent a location of equipotential points. 



For mapping D.C. equipotential lines, a small D.C. generator (1 KVA, 

 200 volts) driven by a gasoline engine (of ample power margin for higher 

 altitudes) is generally employed. Current electrodes are iron pegs, coils 

 of copper wire, or copper screens. Equipotential lines are traced with non- 

 polarized electrodes connected by a wire to a galvanometer. The primary 



