Radio Propagation Over Spherical Earth * 



By CHAS. R. BURROWS 



The paper shews how Watson's solution for the propagation of electro- 

 magnetic waves over perfectly conducting spherical earth merges into the 

 Abraham solution for propagation over a perfectly conducting plane for 

 shorter distances. 



The effects of refraction by the lower atmosphere and of the imperfect 

 conductivity of the earth are taken into consideration. The magnitude of 

 the former, which is appreciable, is obtained. The latter is relatively un- 

 important for ocean water and frequencies of the order of a megacycle and 

 less. 



The theoretical solution for radio propagation over perfectly conducting 

 spherical earth with atmospheric refraction is in agreement with available ex- 

 perimental data for propagation over ocean water for frequencies below a 

 few megacycles. 



Eckersley's extension of Watson's solution to take into account the efifect 

 of the imperfect conductivity of the earth by the phase integral method 

 is found to contain approximations which render its results questionable. 



Theory 



THE electrical disturbance at the surface of the earth due to a 

 vertical dipole has been calculated by G. N. Watson ^ and 

 others. The results for the case of a perfectly conducting spherical 

 earth with transmitter and receiver both situated on the surface may 

 be reduced to the form: 



where p„ and ^n are constants whose values have been calculated as 

 follows: 



Pi = 0.8083 



* Published in I. R. E. Proc, May, 1935. Presented before U. R. S. I. meeting, 

 Washington, D. C, April 26, 1935. 



iG. N. Watson, "The Diffraction of Electric Waves by the Earth," Proc. Roy. 

 Soc. (London) A95, 83-99, October 7, 1918. 



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