MUTUAL IMPEDANCES OF GROUND-RETURN CIRCUITS 639 



although in this case the discrepancy is substantially smaller. On Fig. 

 11 are shown the phase angles of the gradient as computed from the 

 calculated values of resistance and reactance components given on Fig. 

 10. Here also the measured curve falls between the two calculated 

 curves. 



90 



80 



70 



60 



UJ 

 UJ 



o 



UJ 



a 50 



,40 



30 



20 



10 



-10 



200 



400 600 800 1000 1200 



DISTANCE FROM ELECTRODE IN FEET 



1400 



1600 



Fig. 1 1 — Cross Keys tests. Comparison of measured and calculated (from Campbell's 

 formula) angles of mutual impedance gradient. 



Since the gradient near the electrode is obviously affected mainly by 

 the conductivity of the earth in the immediate neighborhood, and that 

 at remote points is influenced more by the conductivity of the earth at 

 substantial depths, the possibility that the earth in this region is not 

 homogeneous, but stratified, is suggested. These curves seem to sup- 

 port the conclusion that the earth in this neighborhood has at least 

 two strata, the upper one having a very low conductivity and the lower 

 one a conductivity approximately a hundred times greater. Further 

 e.xperimental evidence tending to the same conclusion has been ob- 

 tained, and will be described presently. For the present it may be 

 pointed out that this conclusion is supported by the geological data 

 pertaining to this region, for which an upper layer of sand and gravel 

 from 130 to 170 ft. in depth is indicated, superimposed on a mixed 

 structure of sand, clay, and shale, with a substantial amount of ground 

 water. 



Methods Considering A.-C. Distribution of Earth Current. The 

 problem of computing the mutual impedance of ground-return circuits, 

 considering an a.-c. distribution in the earth has been attacked by sev- 



