Addendum to "Radio Propagation Over Plane Earth — Field 



Strength Curves" 



By CHAS. R. BURROWS 



IN the paper of the above title in the January 1937 issue of the Bell 

 System Technical Journal, an approximation which was not ex- 

 plicitly pointed out was made in deriving equation (17). A note from 

 Mr. K. A. Norton* of the Federal Communications Commission points 

 out that equation (17) does not give a reasonable result when r = 1, 

 The explanation is that two terms which are unimportant except near 

 the transmitter when the ground is a perfect dielectric were deleted. 

 The complete equation is 



2E 



W 



1 



1 + r2 ' 1 



1 _ ^g(27r)<i/X)(l-l/T) J _ ^2 g{2Tr id l\){l-l It) 



Irid/X 



(iwid/xy 



(17) 



When r = 1 by virtue of equation (13) W must equal 1/2 and accord- 

 ingly the first term on the right of equation (17) is 1/4. The second 



term gives 1/4 + 



1/4 



and the last term gives 



1/4 



+ 



1/2 



2Trid/\ ""^ ^ ^^ ^^"" ^""" Iwid/X ' (lirid/xy 



Hence when r = 1 equation (17) gives the following relation for the 

 field strength in free space, 



E 



2Eo 



1 , ■ 1/2 



2 lirid/X 



+ 



1/2 



{lirid/xy ' 

 as it should. 



The terms added to equation (17) produce oscillations in the curves 

 of Fig. 3 as shown on the following page. For any physical dielectric 

 the conductivity is not zero and the oscillations disappear at the greater 

 distances giving curves like those of the original Fig. 3. 



Equation (19) should read 



1 



1 + 



1 - T'lirrHd/X 



1 



T'^e 



T0-» 



2Eo. 



(19) 



This increases the deviation of the second factor on the right from unity 



but if the ground is not a perfect dielectric the exponential reduces the 



second factor to unity at the greater distances irrespective of the 



value of e. 



* See the note at the end of " The Propagation of Radio Waves over the Surface 

 of the Earth and in the Upper Atmosphere," Proc. I.R.E., 25, 1203-1236, September, 

 1937. 



574 



