MUTUAL IMPEDANCE OF GROUNDED WIRES 269 



N,{r') = 1 }1 - [1 + (1 + i)/''>-(i+'>'}, 





jQ{r'n)dn, 



the prime accent applied to any length L indicating the corresponding 

 modified length L' = {uv/lpy^L. 



As in formula (A), the six constituent functions involved in formula 

 (C) are arranged in order of importance: first, Qo and iVo, functions 

 only of the modified horizontal distance r'; secondly, Qi and iVi, 

 functions of r' and of the sum of the two modified heights H' and h'; 

 and thirdly, Q2 and iV2, functions of r' and of the numerical difference 

 of the two modified heights. 



To assist in the numerical apphcation of this formula, a table of 

 values of the real and imaginary parts of No has been computed, for 

 all values of r' from to 10, in steps of 0.1. Beyond this range, the 

 function is practically equal to the leading term in its asymptotic 

 expansion, namely, l/r". These computed values are also shown 

 graphically in Fig. 1. The imaginary part changes sign at approxi- 

 mately r' = 3.8, and again at 7.0, oscillating for increasing values of r', 

 although approaching zero very rapidly indeed. 



The real and imaginary parts of the functions Qi{r' ,s') and Ni{r',s') 

 are shown in Figs. 2, 3, 4, and 5, for the range of r' from to 10, and 

 for the set of values of s' from to 0.2 in steps of 0.02. It is believed 

 that this will cover the range of heights likely to be encountered in 

 ordinary problems. To cover this range adequately it was necessary 

 to show portions of the A^i curves with the horizontal scale enlarged 

 two and a half times, and with a greatly reduced vertical scale, in 

 Figs. A:- A and S-A. 



For actual computation, the Q2 and A'2 functions are already ex- 

 pressed in {A) in convenient, closed form, but for purposes of com- 

 parison with Qi and iVi, the corresponding values of Q% and N2 are 

 shown in Figs. 6 and 7, which are drawn to the same scales as Figs. 

 3 and 5. 



Tables II and III give the corresponding numerical values of Qi and 

 A^i for the range of r' from to 1, in steps of 0.1, as well as the values 

 for 1.5 and 2. 



