MUTUAL IMPEDANCES OF GROUND-RETURN CIRCUITS 643 



the grounding electrode could be accounted for on the hypothesis that 

 the earth in this neighborhood is stratified, with a conductivity of 

 around 2.5 X 10~^^ near the surface and 2.5 X 10~^^ in the lower 

 depths. Qualitatively, it is to be expected that with such an earth 

 structure the mutual resistance would be less, and the mutual reactance 

 greater, than the corresponding values for an earth of uniform con- 

 ductivity, since the eddy currents near the surface of the earth will be 

 less, due to the lower earth conductivity. 



0.3 



0,005 



20 30 



50 100 200 300 500 



HORIZONTAL SEPARATION IN FEET 



1000 



Fig. 14 — Cross Keys tests — Carson theory. Comparison between calculated and 

 measured values of mutual resistance and reactance. 



Quantitatively, it would seem that a first approximation to the effect 

 of a stratified earth in which the upper stratum has a much lower con- 

 ductivity than that of the lower region could be obtained by assuming 

 that the currents in the upper layer are negligible and hence that this 

 layer can be abolished. The mutual impedances can then be worked 

 out by the formulas applicable to a homogeneous earth, using the earth 

 conductivity of the lower region and fictitious conductor heights, 

 formed by adding the thickness of the upper stratum to the heights of 

 the conductors above the actual earth's surfaces. Preliminary calcu- 

 lations have been made using this scheme, and it was found that using a 



