640 DELL SYSTEM TECHNICAL JOURNAL 



eral writers.^ In the interpretation of the experimental results, the 

 papers of J. R. Carson ^ and F. Pollaczek '' have been used, since a min- 

 imum of assumptions was made in the solutions advanced by these 

 writers. The assumptions made are that the disturbing circuit is 

 straight and of great length,-' that the propagation constant, in ab- 

 solute units, of the circuit is very small compared to unity, and also 

 that the earth is a homogeneous body of fairly good conductivity. 

 With these assumptions it is found possible to solve the fundamental 

 field equations for the magnetic and electric fields in the vicinity of the 

 disturbing conductor at points remote from the ends of the circuit and 

 thence to get the mutual impedance. Physically, this method recog- 

 nizes and takes into account the fact that in a conductor of large ex- 

 tent, such as the earth, the distribution of alternating current will be 

 influenced by the changing magnetic field. Qualitatively, the effects 

 are similar to those involved in the well-known skin effect, and may be 

 thought of in terms of a distribution of eddy currents in the earth. It 

 is obvious that the distribution of the eddy currents will depend on the 

 earth conductivity and also on the frequency. The resultant fields, 

 and hence the mutual impedances, will then be functions of earth 

 conductivity and of frequency. 



Presentation of the formulas and graphs giving the results of the 

 analysis is outside the scope of the present paper, and reference should 

 be made to the original papers for these. As an illustration of the re- 

 sults, however, the curves of Fig. 12 have been prepared, showing the 

 calculated mutual resistance and reactance of ground-return circuits at 

 a frequency of 60 cycles for several values of earth conductivity, within 

 the range of experimental values. Both the resistance and reactance 

 components are seen to be pronouncedly affected by earth conductivity, 

 particularly for the larger separations. 



In applying this theory to the tests made at Cross Keys, the pro- 

 cedure adopted, in the absence of direct data on the earth conductivity 

 at this location, was to choose an earth conductivity which would result 

 in the best fit between the calculated and observed values, and to see 

 whether a single value for earth conductivity would suffice to explain 

 all the results. On Fig. 13 comparisons have been made between the 

 experimentally determined mutual impedances for the 60- and 500-cycle 

 frequencies; the curves were computed by use of the formulas given by 

 Carson. It will be seen that in so far as the magnitude of the mutual 

 impedance is concerned an excellent agreement can be made between 



' See bibliography references 3 to 9, inc. 

 ' See bibliography. 

 * See bibliography. 

 ^ See bibliography. 



