MUTUAL IMPEDANCES OF GROUNDED CIRCUITS 25 



of 0.5 megohm per centimeter cube. The measurements were not 

 made for the purpose of this comparison, for which they are not well 

 adapted, but they do give both components of the mutual impedance, 

 which is the absolutely essential requirement. The geometrical 

 irregularity of these circuits is shown by Fig. 10. This was com- 

 pletely allowed for by making detailed computations after substitut- 

 ing an approximately equivalent broken line for each circuit. The 

 variability in the earth's resistivity with location, depth and changing 

 moisture content on different days could not be allowed for. The 

 effect of buried gas and water pipes and of other grounded conductors 

 was also necessarily neglected. 



The direct-current theory leaves but one arbitrary constant at our 

 disposal after the frequency and the geometry of the circuits have 

 been fixed. This constant is the earth's resistivity. By trial it 

 was found that 0.5 megohm gave a good average agreement between 

 the calculated resistance components and the entire set of measure- 

 ments, only a part of which is included in Fig. 9. The individual 

 discrepancies are large but are not so large as to be disconcerting, 

 considering the variations in effective earth resistivity from place to 

 place and from day to day during the progress of the tests. 



The calculated reactance component of the mutual impedance 

 based on the direct-current mutual inductance is independent of the 

 earth's resistivity and is uniquely determined by the frequency and 

 geometrical relations. Even a general agreement between the cal- 

 culated and the measured reactances is significant and Fig. 9 shows not 

 only this, but also a great many good individual agreements. The 

 outstanding discrepancies for circuits C and <5* are systematic, and are 

 apparently to be explained by the effective grounding of these cir- 

 cuits at some other points than the midpoints of the track sections. 

 On the basis of this comparison, it appears that the direct-current 

 theory proves itself adequate to give an approximation to the actual 

 mutual reactances, provided the linear scale and the frequency in- 

 volved do not greatly exceed those of these tests. 



Measurements were also made at 60 cycl es - The resistance com- 

 ponent remained roughly the same as for 25 cycles; the reactance 

 component doubled as shown by Fig. 11; each component therefore 

 agreeing approximately with the results which would obtain if the 

 direct-current distribution is maintained. 



Other comparisons have been made with the same conclusion, but 

 tests should be made, throughout a range of frequencies, at a locality 

 where it is known that the conductivity of the upper layer of the 

 earth's surface is reasonably uniform so that the effect of the lower 



