644 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



CONCLUDING REMARKS 



The interpretation of propagation beyond the horizon in terms of re- 

 flection from layers of limited size formed by variations in the gradient 

 of the dielectric constant of the atmosphere leads to relatively simple 

 results which are in good agreement with reported experimental data. 

 The received power depends on the wavelength, the distance, and the 

 size of the antennas used for the circuit and on the strength and size of 

 the reflecting layers. 



As mentioned earlier, the structure of the atmosphere may change 

 markedly from time to time so that large, small and intermediate size 

 layers play their parts at different times. Furthermore, the effective size 

 of a given layer may be different for widely separated wavelengths, de- 

 pending on the roughness of the layer in terms of the wa^■elength. All 

 that can be expected of a study such as the present one is that it serve 

 as a guide for estimating the roles of the various parameters involved in 

 beyond-the-horizon propagation. 



REFERENCES 



1. K. BuUington, Radio Propagation Variations at VHF and UHF, Proc. I.R.E., 



38, p. 27, Jan., 1950. 



2. Proc. I.R.E., Oct., 1955. 



3. H. G. Booker and W. E. Gordon, A Theory of Radio Scattering in the Tropo- 



sphere, Proc. I.R.E., 38, p. 401, April, 1950. 



4. F. Villars and V. F. Weis.skopf , Scattering of EM Waves by Turbulent Atmos- 



pheric Fluctuations, Phys. Rev., 94, p. 232, April, 1954. 



5. C. M. Grain, Survey of Airborne Refractometer ^leasurements, Proc. I.R.E., 



43, p. 1405, Oct., 1955. H. E. Bussej^ and G. Birnbaum, ^leasurement of 

 Variation in Atmospheric Refractive Index with an Airborne Microwave 

 Refractometer, N.B.S. Jour. Res., 51, pp. 171-178, Oct., 1953. 



6. H. T. Friis, A Note on a Simple Transmission Formula, Proc. I.R.E., 34, pp. 



254-56, May, 1946. 



7. S. A. Schelkunoff, Applied Mathematics for luigineers and Scientists, D. Van 



Nostrand Co., Inc., p. 212., 1948, and Remarks Concerning Wave Propagation 

 in Stratified Media, Communication on Pure and Applied Mathematics, 

 4, pp. 117-128, June, 1951. See also, H. Bremmer, The W.K.B. Appro.xima- 

 tion as the First Term of a Geometric-Optical Series, Communication on 

 Pure and Applied Mathematics, 4, pp. 10^115, June, 1951. 



8. K. BuUington, W. J. Inkster and A. L. Durkee, Results of Propagation Tests 



at 505 mc and 4,090 mc on Bejond-Horizon Paths, Proc. I.R.E., 43, pp. 

 1306-1316, Oct., 1955. 



9. K. BuUington, Characteristics of Bej'ond-the-Horizon Radio Transmission, 



Proc. I.R.E., 43, pp. 1175-1180, Oct., 1955. 

 10. J. H. Chisholm, P. A. Portmann, J. T. deBettencourt and J. F. Roche, Inves- 

 tigations of Angular Scattering and Multipath Properties of Tropospheric 

 Propagation of Short Radio Waves Bej'ond the Horizon, Proc. I.R.E., 43, 

 pp. 1317-1335. Oct., 1955. 



