MUTUAL IMPEDANCES OF GROUND-RETURN CIRCUITS 651 



and by a slight extension of the theory, good quantitative agreement 

 can be found. This theory, however, does not explain end effects. 



In the investigation of practical means for enabling the calculation of 

 the mutual impedances of power and telephone lines a scheme involving 

 the experimental determination of a coupling curve has been found to 

 give quite satisfactory results. Further work is to be done on this 

 problem, and similar tests must be made in several other locations be- 

 fore the method can be considered completely satisfactory. Other 

 methods are also being investigated. 



* 



Acknowledgment 



The authors wish to express their appreciation of the assistance of 

 Messrs. F. J. Grueter and B. C. Griffith in the field testing, analysis 

 of the data and preparation of this paper, also to many others who have 

 aided in this work. Thanks are due to the operating power and tele- 

 phone companies who lent the facilities for some of the work described, 

 and to members of their organizations who assisted in the tests. 



Bibliography 



The following list is far from complete, but covers the more important 

 papers which were consulted in the course of the work: 



1. California Railroad Commission, Inductive Interference, 1919. 



2. G. A. Campbell, "Mutual Impedances of Grounded Circuits," The Bell System 



Technical Journal, 2, October 1923, pp. 1-30. 



3. F. Breisig, "Ueber die Berechnung der Magnetischen Inducktion und Wechsel- 



stromleitungen mit Erdruckleitung," Telegraphen und Fernsprechtechnik, 14, 

 April 1925, pp. 93-98. 



4. O. Mayr, "Die Erde als Wechselstromleiter," E. T. Z., 46., September 1925 pp. 



1352-1436. 



5. R. Rudenberg, "Die Ausbreitung der Erdstrome in der Umgebung von Wechel- 



stromleitungen," Zeit. fur Angew. Math, und Aleck., 5, October 1925, pp. 361- 

 389. 



6. F. Pollaczek, "Ueber das Feld einer Unendlich Langen Wechelstrom Durch 



Flossenen Einfachleitung." Elektrische Nachrichten Technik, 3, September 

 1926, pp. 339-359; 4, January 1927, pp. 18-30. 



7. J. R. Carson, "Wave Propagation in Overhead Wires with Ground Return," 



The Bell System Technical Journal, 5, October 1926, pp, 539-554. 



8. G. Haberland, "Theorie der Leitung von Wechelstrom Durch die Erde," Zeit. 



fur Angew. Math, und Mech., 6, October 1926, pp. 366-379. 



9. F. Pollaczek, " Gegenseitige Induktion Zwischen Wechselstromleitungen von 



Endliche Lange, A nn. der Physik, Vol. 87, Dec. 1928, pp. 965-999. This paper 

 treats of the mutual impedances of circuits of finite length. However, the 

 assumptions regarding conditions at the ground connection seem to depart con- 

 siderably from the practical conditions of the experiments reported in the pres- 

 ent paper. For this reason, and the fact that numerical evaluations by these 

 formulas are very laborious, no calculations by this method have as yet been 

 made for comparison with the experimental results. 



