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BELL SYSTEM TECHNICAL JOURNAL 



(that is, in inverse ratio to their capacitance values). The induced 

 voltage on the telephone wire may therefore be expressed mathe- 

 matically as: 



7- Ctp 



Cto + Cj 



Er. 



Where there are numerous power and telephone wires, capacitances 

 exist between every possible combination of wires, and of wires and 

 ground, resulting in a complicated network, but the principles involved 

 are the same as in the simple case discussed above. 



^\^- 



PLANE 



REPRESENTING 



SURFACE OF 



GROUND 



Fig. 2 — Fundamental of electric induction. 



The point of particular interest is that the potential of the telephone 

 wire tends to be the same all along its length and, if it is perfectly 

 insulated from ground, extends only through the length of the exposure, 

 and has no equipment on it, this potential is independent of the length 

 of the exposure (this is the condition shown in Fig. 2 if the impedances 

 to ground are neglected). This is because, while all of the capacitances 

 in the above equation are proportional to exposure length, the ratio 



-7\ —j:, — is independent of length. However, in the usual field 



(-'TO ~r ^TP 



case, the circuits extend beyond the exposure and have equipment 

 connected between them and ground so that there are impedances to 

 ground outside the exposure (as shown dotted in Hg. 2) through 



