126 BELL SYSTEM TECHNICAL JOURNAL 



The fundamental similarity of visual light and radio waves makes it 

 obvious that somewhere between these regions a transition region must 

 occur in which the apparently different phenomena merge into each 

 other. In theoretical studies of this region it is necessary to use con- 

 cepts borrowed from both the adjacent frequency ranges. A survey 

 of a part of this field has now been in progress for some time and some 

 of the results obtained to date are given in this paper and in a com- 

 panion paper by Englund, Crawford and Mumford. 



Since the Kennelly-Heaviside layers do not reflect ultra-short 

 waves sufficiently to be a factor in the ordinary phenomena of this 

 range, our interest is confined to the "ground" or direct wave. This 

 term refers to any and all signals which arrive at the receiver except 

 those which are affected by the upper atmosphere. It is otherwise non- 

 committal as to the mechanism of transmission. The physical pictures 

 of this mechanism which have been so useful in the case of long waves 

 are of little help when the length of the wave is of the order of, or 

 smaller than, the dimensions of irregularities of topography which it 

 encounters. The well-known work of Abraham,^ Zenneck,^ Sommer- 

 feld ^ and the more recent studies by Weyl,"* Eckersley,^ Strutt,^ and 

 Wise '' apply to special cases of ultra-short wave propagation, but 

 generally speaking help but little in the more numerous problems where 

 irregularity of topography is the rule. Likewise, the important work 

 of Watson ^ and of Van der Pol ^ may perhaps find application in the 

 diffraction problems of ultra-short waves, but only to a limited 

 extent. 



It is obvious that rigorous solutions of problems in transmission 

 over rough surfaces are out of the question, but progress can be made 

 by way of the general concepts of reflection, diffraction and refraction. 

 We shall endeavor to show that many phenomena observed can be 



* Abraham, M., Enz. d. math. Wissen., 5, Art. 18. 



2 Zenneck, J., " Uber die Fortpflanzung ebenen elektromagnetischer Wellen langs 

 einer ebenen Leiterflache und ihre Beziehung zur drahtlosen Telegraphie," Ann. d. 

 Phys., 4, 23, 846 (1907). 



^ Sommerfeld, Arnold, "Uber die Ausbreitung der Wellen der Drahtlosen Tele- 

 graphic," Ann. d. Phys., 4, 28, 665-736, Mar. 1909, and "Ausbreitung der Wellen 

 in der drahtlosen Telegraphie. Einfluss der Bodenbeschaffenheit auf gerichtete und 

 ungerichtete Wellenzuge," Jahr. d. drahtlosen, Tel. u. Tel., 4, 157 (1911). 



^ Weyl, H., "Ausbreitung elektromagnetischer Wellen iiber einer ebenen Leiter," 

 Ann. d. Phys., 4, 60, 481-500 (1919). 



^ Eckersley, T. L., "Short-Wave Wireless Telegraphy," Jour. I. E. E., 65, 600- 

 644, June 1927. 



•* Strutt, M. J. O., "Strahlung von Antennen unter dem Einfluss der Erdboden- 

 eigenschaften," Attn. d. Phys., 5, 1, 721-772 (1929); 4, 1-16 (1930); 9, 67-91 (1931). 



^ Wise, W. Howard, "Asymptotic Dipole Radiation Formulas," Bell Sys. Tech. 

 Jour., 8, 662-671, Oct. 1929. 



" Watson, G. N., "The Diffraction of Electric Waves by the Earth," Proc. Rov. 

 Sac. (London), 95, 83-99, Oct. 7, 1918. Van der Pol, Balth., "On the Propagation 

 of Electromagnetic Waves Around the Earth," Phil. Mag., 6, 38, 365-380, Sept. 1919. 



