Addendum to 'Radio Propagation Over Plane Earth - Field Stength Curves'

N the paper of the above title in the January 1937 issue of the Bell System Technical Journal, an approximation which was not explicitly 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 t h a t two terms which are unimportant except near the transmitter when the ground is a perfect dielectric were deleted. The complete equation is E 2E W 1 + T2 1 - r4[ M/X 1 (27rid/y J' ^ When r = 1 by virtue of equation (13) W must equal 1/2 and accordingly the first term on the right of equation (17) is 1/4. The second term gives 1/4 + ^ and the last term gives J g j + j J ^ · Hence when r = 1 equation (17) gives the following relation for the field strength in free space, E _ 1 1/2 1/2 2Eo 2 ~r 2irid/ ^ (2irid/)2' 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 2vid / _ IN Mr^ferxH1-^ ]2£°- (19)