MUTUAL IMPEDANCES OF GROUNDED CIRCUITS 



i r Ba 



= ?> dx = \(Ba-Aa). 



ds 



s 2 



Table I 



Entries are the value of k in the formula N = kA for the Neumann integral between 



the specified flows, A = — Aa-\-Ab+Ba — Bb, or 2AB if A =a, B = b, and points A 



B, a, b are all on the earth's surface. 



* Not of the assumed form and in general infinite. 



t Each type of flow is designated by a script letter. Any flow in the surface of 

 the earth, assumed to be a plane, is designated by Jf, there being no restriction on 

 the number of filaments of current but each filament must start from a common 

 point, A, and extends to another common point, B. A special case of JIT" is ^"the 

 horizon return flow made up of two superposed uniform radial flows, from A to 

 every point of the horizon and back to B. The space return flow, S, is made up 

 of two superposed uniform radial flows, one outward in all directions from the point 

 A and the other inward from all directions toward the point B. The earth return 

 and air return flows, £ and Jf, are similar except that the flows are uniformly dis- 

 tributed over all directions in the earth and air, respectively. The nadir return 

 and zenith return flows, 9/ and «>Z°, consist of two infinite vertical filaments from A 

 and back to B by way of the nadir and zenith, respectively. Small script letters 

 indicate similar types of flow with any independent terminal points, a and b. Dif- 

 ferences such as (Jf—S) designate closed flows; thus (JfT—S) designates any flow 

 on the earth's surface from A to B where it enters the earth and after spreading 

 out uniformly through the earth returns to the terminal A, thus closing the flow. 



