RADIO PROPAGATION OVER SPHERICAL EARTH 



485 



conducting plane earth based on the solution by Sommerfeld/'' 

 Weyl/^ Wise ^^ and others and evaluated by Rolf,^^ for the corre- 

 sponding values of a^'^X^""' indicated on the curves.'^ The part of 

 curve // shown also coincides with the solution for perfectly conducting 

 plane earth as determined by Abraham.* This indicates that for 

 conductivities greater than those for which a^'^X^'^ = 10"'' the earth 

 may be regarded as a perfectly conducting sphere. 



The fact that the plane earth solution for values of the parameter 

 of the order of 10~'^ and less (curves E and F) gives lower fields than 

 Eckersley's solution for spherical earth indicates that the approxima- 

 tions made introduce large errors in these regions of the solution. 

 This inconsistency between the Eckersley solution and the rigorous 

 solution for plane earth in itself would indicate that the solution is 



!^ 20 



\n 30 



5 90 

 o 



Q 100 



100 1000 



x = d/\/X (d&XiN KILOMETERS) 



10,000 



Fig. 6 — Comparison of theoretical curves for radio propagation. The numbers on 

 the curves indicate the value of o-i'^X^/o for the case represented by the curve in 

 question (conductivity in electromagnetic units and wave-length in kilometers). 



'^ A. Sommerfeld, "Uber die Aursbreitung der Wellen in der drahtiosen Telegra- 

 phic," Ann. der Phys. 4, 28, 665-736, March 16, 1909 and "Ausbreitung der Wellen in 

 der drahtiosen Telegraphic. Einfluss der Bodenbeschaffenheit auf gerichtetc und 

 ungerichtcte wellenzuge." Jahr. d. drahtiosen T. 4, 157-176, December, 1910. 



1^ H. Weyl, "Ausbreitung elektromagnetischen Wellen iiber eineni ebenen Leiter," 

 Ann. der Phys. 4, 60, 481-500, November 20, 1919. 



'^ W. Howard Wise, "The Grounded Condenser Antenna Radiation Formula," 

 Proc. I.R.E. 19, 1684-1689, September, 1933. 



1' B. Rolf, "Graphs to Prof. Sommerfeld's Attenuation Formula for Radio 

 Waves," Proc. I.R.E. 18, 391-402, March, 1930. 



'8 The usual parameter, aX^, that occurs when the field over imperfectly conducting 

 plane earth is plotted against distance, becomes crX"'/^ or (cr"^ a^"')^ when the field is 

 plotted against d\~^^^. 



