MUTUAL IMPEDANCES OF GROUND-RETURN CIRCUITS 637 



as the frequency is decreased, the agreement is far from good at 60 

 cycles, the lowest frequency used in these tests. 



In the immediate vicinity of the grounding electrode on the disturb- 

 ing circuit, however, the experimental observations of mutual imped- 

 ance gradient can be explained fairly well in terms of a d.-c. distribu- 

 tion. The curves of Figs. 5 and 6 show that in the immediate neigh- 

 borhood of the electrode, the gradient along any radius diverging from 

 the electrode decreases ver}' rapidly with increase in distance from the 



180 



I- 



UJ 



Hi 160 



o 

 o 

 If) 



£i.*o 



CL 



I 120 



UJ 



X 



o 

 oioo 



lu 80 

 U 



z 

 < 



O 60 



3 

 Q 



Z 



_l 40 

 < 



D 

 (- 



2 20 



20 



30 



50 100 200 300 



HORIZONTAL SEPARATION IN FEET 



500 



1000 



Fig. 9 — Cross Keys tests. Campbell theory comparison of measured and calculated 



mutual inductances. 



electrode, and is approximately in phase with the current. The gra- 

 dient along the radius under the disturbing line approaches asymptoti- 

 cally a constant value, and beyond 300 ft. from the electrode the phase 

 angle changes rapidly from a very small value to a value approximating 

 80 degrees. The gradient along the other radii, however, appears to 

 decrease indefinitely and the phase angles are smaller. Such effects 

 are in qualitative accord with predictions based on a d.-c. distribution, 

 as will be seen by reference to Figs. 10 and 11. 



On Fig. 10 are plotted the resistance and reactance components of 

 the observed gradient under the disturbing line, with values computed 

 using Campbell's formulas. Two calculated curves for the resistance 



