MUTUAL IMPEDANCES OF GROUND-RETURN CIRCUITS 633 



parallel circuit was closely proportional to the length of the circuit and 

 that the voltage induced in a ground-return circuit extending perpen- 

 dicular to the disturbing line was exceedingly small. 



As the points of grounding on the disturbed circuits approached those 

 of the disturbing circuit this proportionality no longer existed nor was 

 the voltage in a perpendicular circuit of negligible magnitude. A second 

 series of tests was therefore conducted to determine the nature of this 

 effect and the area in which it was of importance. 



In these tests voltages were measured in very short disturbed circuits 

 extended along radii converging on the ground electrodes on the dis- 

 turbing line. At each location the circuit was made progressively 

 shorter until the quantity measured per unit length was practically 

 independent of the length. Thus the gradient of the mutual im- 

 pedance, in the direction of the radius at the point of measurement was 

 determined. These measurements were made only at a frequency of 

 60 cycles. 



80 



70 



HJeo 

 o 50 



40 



ui 30 



O 



20 



5 10 



I 



0. 



-10 



200 



400 



600 800 1000 1200 



DISTANCE FROM ELECTRODE IN FEET 



1400 



1600 



1800 



Fig. 6 — Cross Keys tests. Phase angle of mutual impedance gradient in vicinity of 

 grounding electrode. Experimental curves. 



The resulting observations are shown in Figs. 5 and 6. Fig. 5 shows 

 the magnitude of the mutual impedance gradient along three radii, 

 one radius being directly under the disturbing line, the second perpen- 

 dicular to it, and the third along the extension of the line. Fig. 6 

 shows the corresponding phase angles. Under the disturbing line, as 

 the distance from the grounding point is increased, the gradient ap- 

 proaches a constant value and the phase angle changes rapidly from 

 a very small value to an angle approaching 80 degrees. Along the 

 latter two radii, however, the magnitude of the gradient appears to 

 decrease indefinitely and the phase angles are smaller. 



