PROPAGATION OF PERIODIC CURRENTS 507 



currents induced in wires No. 1 and No. 2 due to the reactions in the 

 system. 



It will be observed that, if the system were ideally balanced, no 

 currents would be induced in the neighboring wires and we should 

 simply have the current I^ in the metallic circuit; in engineering 

 language there would be no crosstalk. This is the ideal to which the 

 correctly designed telephone system approximates by means of 'trans- 

 positions.' It is never, of course, completely realized but the approxi- 

 mation, as regards the neighboring metallic circuits, must be extremely 

 close, since the allowable amount of crosstalk is very small. 



Let us now return to the original system of equations for n parallel 

 wires discussed in Section I and let us write /i = 7" + J/, 

 /2 = — 7° + li and replace I2, I3 • • • In hy h', I3' • • • /„' respec- 

 tively, the primes indicating that the currents are 'unbalance' currents. 

 Similarly write Fi = F« -f F/, F2 = - F" -f F2'; Qi = Q' + Qi\ 

 Q2 = — (2" + Q2', and for the rest of the wires add primes to the 

 symbols for potential and charge. Equations (2) may then be 

 written as 



dV ' 

 (211 -j- Z\\)I\ -\ — -^ — = — Z12I2 — Z\zlz — Zuli — ' ' • , 



(^22 + ■2^22)72 -\ -T~~ = ~ Z21I1 — Z23I3 ~ Z^ili ~ ' ' ' ) 



(2,, + Z,y)7/ -f ^' = - {Zn - Z,2)I' - Znh' 



(j = 3, 4 • • • »), 



or, denoting the right hand sides of the equations by //, f-i!, //, 

 respectively, 



(S22+Z22)72'+^=/2', ^33^ 



(34) 



{Zji + Zjjjl j -\- J — Ji 1 



(j = 3, 4 • • • n). 



This set of equations in the unbalance currents 7/, • • • In and 

 unbalance potentials F/, • • • Vn admits of immediate interpretation. 

 This is to the effect that the unbalance currents may be regarded as 

 due to an impressed field characterized by an axial electric intensity 



