This paper presents a formula for the mutual impedance of long grounded wires above the surface of the earth, on the assumption that the conductivity of the earth varies exponentially with depth according to the formula . For b=0 the formula reduces to the known result for a uniformly conducting earth, while if b is allowed to become negatively infinite it reduces to the result for an earth consisting of a conducting layer at the surface only. For small values of b the first terms in the expansion of the impedance formula in powers of b are obtained, and curves are included of the real and imaginary parts of the coefficient of b.
REFERENCES
1.
2.
3.
4.
5.
6.
A similar assumption has been made recently by
G. J.
Elias
, Elekt. Nachr. Tech.
8
, 4
–22
(1931
), in connection with a different problem.7.
G. N. Watson, Theory of Bessel Functions, Cambridge, 1922, page 78.
8.
Reference 5, page 1583.
9.
Reference 7, page 77.
10.
Reference 1, formula (23b);
reference 2, formula (24);
reference 4, formula (18).
11.
Reference 3, formula (13). To obtain Mayr’s formula we have to put in Eq. (15).
12.
Reference 2, formulae (32) and (33).
13.
See e.g., E. T. Whittaker and G. N. Watson, Modern Analysis, Third Edition, Cambridge, 1920, page 241. When n is an integer where γ is Euler’s constant and has the value 0.57722.
14.
In drawing the curves for and use was made of the tables of values published by
J. E.
Clem
, Trans. Amer. Inst. Elect. Eng.
50
, 909
–910
(1931
).15.
Tables of values of these functions have been published by
H. B.
Dwight
, Trans. Amer. Inst. Elect. Eng.
48
, 812
(1929
).
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© 1933 American Institute of Physics.
1933
American Institute of Physics
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