140 BELL SYSTEM TECHNICAL JOURNAL 



The radio curves are based on the famihar Austin-Cohen formula: 



^ = Rd 



where / = amperes 

 R = ohms 

 h = meters 

 / = cycles 

 d = miles 



Taking equal antenna heights at two ends h^ = K. 



As regards antenna resistance we assume symmetry as between 

 the two ends, and that the external (radiation) resistance of the an- 

 tenna equals the resistance within the antenna (which resistance 

 would be internal apparatus resistance in the case of a perfect an- 

 tenna). This makes R^ (radiation resistance) = i?,- (ohmic resistance) ; 

 and R of (1) becomes = R^ -^ Ri where: 



Rr = 17.8 X 10-1* h^f. (2) 



Expressing in terms of current ratio and substituting values of R, 

 equation (1) becomes, 



^ = 45.5 X 10-V^. e^-*^^'^"''^^^ (3) 



Ir 



In order to plot this equation on the same basis as we usually plot 

 wire attenuation, the logarithm of the ratio is used, thus; 



T 4 4 V 10~s /— 



logio j^ = logio 45.5 X 10-' fd + • ^ 3Q3 d Vf (4) 



which is the equation of the curves plotted. 



The ratio of the currents in the two antennas is in this case a true 

 measure of the transmission because they are in circuits of equal im- 

 pedances, by the assumption of antenna symmetry. 



Data for the Wire Curves 



R IC , G IL 

 = 2 \ L + 2 \ C' 



For number 8 Birmingham wire gauge open wire (diam. = 0.165 

 in. = 4.19mm. wire spacing = 12 in. = 30.5 cm. 40 poles per mile) 

 dry weather, the constants per mile are; 



L = 3,370 ^lh. 

 C = 9,140 mm/. 



