4 BELL SYSTEM TECHNICAL JOURNAL 



= 21 rr l tan (a/2). Above the horizon plane there is no magnetic 

 field, since any magnetic lines of force are, by symmetry, horizontal 

 circles and the intensity is zero, since there is no current threading 

 any horizontal circle above the surface of the earth. 



Superposing this closed flow and a similar closed flow through B 

 from the earth to the horizon plane, we obtain a closed flow from A 



-7 -.6 -.5 -A 



I .2 .3 A .5 .6 .7 & 9 1.0. 



Fig. 1 — Flow and equipotential lines on the earth's surface for an earth return flow 

 from A to B. C/I is the fraction of the current flowing in the earth outside the 

 flow surface of revolution; V/I is the resistance to the flow of the portion of the 

 earth lying between the equipotential surface of revolution and the mid or zero po- 

 tential plane, if the earth's resistivity is p = 2w. The flow and equipotential lines 

 through each point on the dotted curve are perpendicular and parallel, respectively, 



to AB 



to B in the earth and back from B to A in the horizon plane. The 

 magnetic field for this closed flow, being the sum of the magnetic 

 fields for the component flows, will be zero above the horizon plane, 

 while below it will consist of lines of force in horizontal planes. This. 



