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velocity, phase velocity, and index of refraction of the propagation medium. Physical significance cannot be attributed to the immediate region of the source because velocities, e, in excess of the constant c, or indices, 71, less than 1, would be contrary to the principle of relativity.

5. Bibliography

[1] K. A. Norton, The calculation of the ground wave field intensity over a finitely conducting spherical earth, Proc. IRE 29, No. 12, p. 623–639 (December 1941).

[2] K. A. Norton, The physical reality of space and surface waves in the radiation field of radio antennas, Pt. III, Proc. IRE 25, No. 9, 1192-1202 (September 1937).

[3] K. A. Norton, The propagation of radio waves over the surface of the earth and in the upper atmosphere, Proc. IRE 25, No. 9, 1203-1236 (September 1937).

[4] K. A. Norton, The propagation of radio waves over the surface of the earth and in the upper atmosphere, Pt I, Proc. IRE 24, No. 10, 1337-1387 (October 1936).

[5] K. A. Norton, Propagation in the FM and broadcast band, Advances in Electronics, vol. I (Academic Press Inc., New York 10, N. Y., 1948).

[6] Balth van der Pol and H. Bremmer, The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow, Natuurkundig Laboratorium der H. V. Philips Gloeilampen Fabriken, Eindhoven, Holland; Phil. Mag. [7] 24, Pt. I, 141 (July 1937); pt. II, 825 (Nov. 1937); Supp. J. Science 25, 817 (June 1938). [7] H. Bremmer, Terrestrial radio waves; theory of propagation (Elsevier Publ. Co., New York, N. Y., 1949). [8] G. N. Watson, The diffraction of electric waves by the earth and the transmission of electric waves round the earth, Proc. Roy. Soc. (London) [A] XCV, 83 (1918); and [A] XCV, 546 (1919).

[9] W. H. Wise, Condenser antenna radiation, Proc. IRE 19, No. 9, 1684 (1931).

[10] W. H. Wise, Asymptotic dipole radiation formulas, Bell System Tech. J. VIII, No. 4, 662 (October 1929). [11] A. Sommerfeld, Uber die Ausbreitung der Wellen in der drahtlosen Telegraphie, Ann. Physik, Vierte Folge, Band 28, No. 4 (1909).

[12] The Staff of the Computation Laboratory, Tables of modified Hankel functions of order one-third and of their derivatives (Harvard Univ. Press, Cambridge, Mass., 1945).

[13] J. C. P. Miller, The Airy integral, giving tables of solutions of differential equation y'=ry, Math Tables Part-vol. B, British Assoc. for Adv. of Sci., Table III, B-43 (Univ. Press, Cambridge, 1946).

[14] E. F. Florman, NBS Tech. News Bul. 39, No. 1, p. 1–3 (January 1955).

[15] B. van der Pol and K. F. Niessen, The propagation of electromagnetic waves over a level ground, Ann. Physik [5] 6, No. 3, 273-294 (1930).

[16] J. R. Wait, Radiation from a vertical electric dipole over a stratified ground, pt. I, Trans. Inst. Radio Engrs., PGAP-1, No. 1, p. 9-11 (July 1953); also, J. R. Wait and W. C. G. Fraser, Radiation from a vertical electric dipole over a stratified ground, pt. II, Trans. Inst. Radio Engrs., PGAP-2, No. 4, p. 144-146 (October 1954).

[17] Physical constants and conversion factors, 4th ed. (Office of Naval Research, Dept. of the Navy, Washington, D. C., Sept. 1953).

[18] H. von Hoerschelmann, Über der Wirkungsweise des geknickten Marconischen Senders in der drahtlosen Telegraphie, Jahrbuch der drahtlosen Telegraphie and Telephonie 5, 14-34 (Barth, Leipzig, 1912). [19] G. Kirchoff, Zur Theorie der Lichtstrahlen, Ann. Physik und Chemie, Newe Folge, Band XVIII, p. 663 (Leipzig, 1883).

[20] H. Hertz, Die Kräfte elektrischer Schwingungen behandelt nach der Maxwell'schen Theorie, Ann. Physik und Chemie, Newe Folge, Band XXXVI, p. 1 (Leipzig, 1889).

[21] J. R. Wait and L. L. Campbell, Transmission curves for ground wave propagation at low radio frequencies, Radio Physics Laboratory, Rept. No. R-1 (Defense Research Telecommunications Dept., Ottawa, Canada, April 1953).

[22] A. B. Schneider, Phase variations with range of the ground wave signal from C. W. transmitters in the 70-130 kc/s band, J. British Inst. Radio Engrs. 12, No. 3, 181–194 (March 1955). (Decca.)

[23] G. Millington and J. C. Thackray, Ground wave propagation curves for frequencies from 150 ke/s to 10 Mc/s, Marconi Review, No. 110, 3d Quarter, vol. XVI (1953).

[24] H. A. Lorentz, The theory of electrons and its applications to the phenomena of light and radiant heat (G. E. Stechert and Co., New York, N. Y., 1906, 1923).

[25] G. N. Watson, A treatise on the theory of Bessel functions, p. 229 (Macmillan Co., New York, N. Y., 1948). [26] J. R. Wait and H. H. Howe, Amplitude and phase curves for ground wave propagation in the band 200 cycles per second to 500 kilocycles, NBS Circular 574 (1956).

[27] B. G. Pressy, G. E. Ashwell, and C. S. Fowler, The measurement of the phase velocity of ground wave propagation at low frequencies over a land path, Proc. Inst. Elec. Engrs. 100, pt. III, 73-84 (1953). [28] A. Sommerfeld, Über die Fortpflanzung des Lichtes in dispergierenden Medien, Ann. Physik, Vierte Folge, Band 44, No. 10, p. 177-202 (1914).

[29] L. Brillouin, Über die Fortpflanzung des Lichtes in dispergierenden Medien, Ann. Physik, Vierte Folge, Band 44, No. 10, p. 203-240 (1914).

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Phase, c, of Secondary Factor, F, Microseconds

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Distance From Source, Statute Miles

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FIGURE 4. Phase variation of

secondary factor with distance for various a factors.

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Phase, tc, of Secondary Factor, F, Microseconds

Phose, tc, of Secondary Factor, F, Aloft Relative to Surface Value, Microseconds

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Conductivity, σ, Mhos per Meter

FIGURE 7. Effect of conductivity on phase of secondary factor at various distances from source.

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