MUTUAL IMPEDANCE OF GROUNDED WIRES 



281 



For very large values of r' it is convenient to express the functions 

 as follows: 



<2o(/-') + Q,{r\s') = Qo{r') ^ 

 No{r') + Nrir',s') = No{r') \ 



Qo{r') ^ 



rn Krj_ , . 



(- (8) 



The real and imaginary parts of these ratios of functions — the coeffi- 

 cients of s' in the above expansions — are shown in Figs. 12 and 13. 

 We note that each of these ratios approaches the value (1 + i) as r' 

 increases without limit. Hence, as a rough approximation, we may 

 say that the mutual impedance for wires at heights H and h, with 

 separations large in comparison with these heights, is equal to the 

 impedance for wires at zero heights multiplied by the factor: 



1 + (1 + i){H' + h') = 1 + r(// + h). 



(9) 



The mutual impedance formula (A) was originally derived from 

 first principles, following the method used in the previous paper for 



a: 0.7 



O 0.5 



g 0.4 

 < 



3 4 5 6 



VALUES OF r' 



Fig. 8 — Real and imaginary parts of (2i '■"(''')• 



