MUTUAL IMPEDANCES OF GROUNDED CIRCUITS 



13 



the numerical magnitude of these Neumann integrals between grounded 

 circuits. In order to visualize the magnitudes involved and supply 

 means by which they may be readily calculated, a number of diagrams 

 have been prepared for the important case of straight conductors. 5 



8 







8 



10 



Fig. 4 — 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 = 2tt. The numerator and denominator of the bracketed fraction on each section 

 of the curve show the factors by which the vertical and horizontal scales must be 

 multiplied for use on this section 



If the two straight conductors OA, Oa start from a common point 

 0, the mutual Neumann integral is shown by Fig. 2; the curves give 

 the locus of terminal a for constant values of the integral when the 

 other conductor OA is the unit base. The Neumann integral between 



6 The necessary formulas are given in the paper loc. cit. Additional transforma- 

 tions of these formulas are given in the appendix to the present paper. 



