552 BELL SYSTEM TECHNICAL JOURNAL 



Correspondingly, r = 2h\/^ has the values 4.0 and 0.4, respectively. 

 Reference to the preceding formulas and curves for /, for r = 4.0 and 

 r = 0.4, give 



J = 0.126+i 0.168, X = 10-12 



/=0.323+«' 0.871, X = 10-14 



whence the corresponding values of Z' are 



Z' = 4co. (0.12G+i 0.168), 

 Z' = 4w. (0.323+^0.871). 



These are the "ground return" impedances per unit length in elm. 

 c.g.s. units; to convert to ohms per mile they are to be multiplied by the 

 factor 1.61X10-*. Consequently setting co = 7^.10^ we get 



Z' = 6.447r(1.3+z 1.7), X - 10-12 



Z' = 6.447r (3.2+^8.7), \ = lO-'\ 



Comparison of these formulas shows that an hundred-fold increase 

 in the resistivity of the ground increases the resistance component of 

 the ground return impedance by the factor 2.5 and increases its 

 reactance only five-fold. That is to say, the ground return impedance 

 is not sensitive to wide variations in the resistivity of the earth, a 

 fortunate circumstance in view of its wide variability and our lack of 

 precise information regarding it. 



Induction from Electric Railway Systems 



A particularly important application of the preceding analysis is 

 to the problems connected with the disturbances induced in parallel 

 communication lines by alternating current electric railways. As- 

 suming the frequency as 25 c.p.s., we have corresponding to X = 10-i2 

 andX-10-iS 



~ 0.45X10-4 and 0.45 XlO-^ 



Taking the height of the trolley ware as approximately 30 ft., // = 10^ 

 and assuming the parallel telephone as the same height above ground 

 and separated by approximately 120 ft., .'v; = 4.10^ and 



= 4.47X10''V^ 



