478 BELL SYSTEM TECHNICAL JOURNAL 



circuit composed of the power wires in parallel with ground return and 

 the circuit composed of the telephone conductors in parallel with ground 

 return. This is because, while the power to customers is usually 

 transmitted over metallic power circuits and telephone conversations 

 between telephone customers are usually over metallic telephone cir- 

 cuits, the circuits composed of the wires and ground in both systems 

 enter into the induction picture unless the systems are perfectly 

 balanced (which, as pointed out previously, is impracticable). 



Considering the power system first, it is customary to divide the line 

 currents and voltages into residual and balanced components. The 

 balanced currents are the components which add up vectorially to 

 zero. The residual current is the vector sum of the line currents and is 

 that which remains after the balanced components are taken out. 

 Similarly, the balanced voltages are the components of the voltages to 

 ground which add up vectorially to zero and the residual voltage is the 

 vector sum of the voltages to ground. 



Thus it is seen that the balanced voltages and balanced currents are 

 confined to the line wires while the residuals act in the circuit composed 

 of the line wires in parallel wdth earth return. For a three-phase circuit 

 the effect is that of a single-phase voltage equal to one third the residual 

 voltage applied between the line wires and earth and a single-phase 

 current equal to the residual current flowing out in the three phase 

 wares in parallel and returning via the earth (or metallic paths other 

 than the phase wires if such exist). 



Whether appreciable residuals exist on the power system depends on 

 many conditions, some of which are discussed later. 



Considering the telephone circuit, the voltages, as pointed out in con- 

 nection with the discussion of the theory of magnetic and electric in- 

 duction, exist along the conductors or between them and earth. How- 

 ever, these voltages may not be identical for the two conductors of a 

 metallic circuit and the vector difference exists as a voltage acting 

 between the two wires. This voltage which, of course, tends to 

 send current around the metallic circuit (and hence noise in the re- 

 ceivers at the ends of the circuit), is often spoken of as due to "direct 

 metallic-circuit induction." The average of the voltages between the 

 two wires and earth is often spoken of as "voltage to ground" and the 

 currents in the two wires in parallel are often spoken of as " longitudinal- 

 circuit" currents. The effects of these voltages to ground and longi- 

 tudinal-circuit currents on telephone circuits which are not perfectly 

 balanced are discussed later. 



All of the factors which have been mentioned, that is, balanced and 

 residual components, direct metallic induction, longitudinal circuit 



