14 



BELL SYSTEM TECHNICAL JOURNAL 



any two straight filaments & and r having terminals A, B and a, b 

 may be expressed as 



Ns?r = N {Aa) - N {Ab) - N {B a) + N (Bb) , 



(6) 



where N { Aa) stands for the Neumann integral between the two straight 

 filaments, OA and Oa, beginning at 0, the point of intersection of & 

 and /•, extended if necessary, and ending at the terminals A and a; thus 



io - * iO"" io"* po" 3 iO" 1 j 



I 10 IO 2 K> s 10* 10* 10* 



Fig. 5 — Mutual Neumann integral between filaments forming opposite sides of a 



rectangle with unit separation. The dashed curves show the mutual resistance 



between the filaments if the circuits are grounded through the earth and its resistivity 



is p = 27r. This is Fig. 4, but with logarithmic scales 



the integral between any two filaments which would intersect within 

 a finite distance may be readily found after reading four values from 

 Fig. 2. 



In the special case of parallel filaments Fig. 2 fails; the corresponding 

 curves for this case are presented by Fig. 3, which assumes a unit base 

 filament and a parallel filament starting at a point on the left hand 

 perpendicular to the base. Differences will give the general case 



