Self-induction of Wires. 83 



have the formula (1/), giving a slightly greater value. The 

 effective resistance is of course the sum of the resistances, and 

 the effective leakage resistance would be the sum of the leak- 

 age resistances of the two wires with respect to earth, if that 

 were the only way of getting leakage between the wires, but 

 it must be modified in its measure b}^ leakage being mostly 

 from wire to wire over the insulators, arms, and only a part 

 of the poles. 



But, if there be any inequalities between the wires, diffe- 

 rential effects will result, due to the presence of the earth, in 

 spite of its little influence on the value of the effective capacity ; 

 whereby the current in one wire is made to be not of the same 

 strength as in the other, and the charge on one wire not to 

 be the negative of that on the other. The propagation of 

 signals from end to end of the looped-circuit will not then 

 take place exactly in the same manner as in a single wire. 

 To allow for this, we may either bring in the full comprehen- 

 sive system of electrical constants and variables ; or, perhaps 

 better, exhibit the differential effects separately by taking for 

 variables the sum of the potentials of the wires (taking earth 

 at zero potential) and half the difference of the strength of 

 current in them, in addition to the difference of potential of 

 the wires and half the sum of the current strengths, which 

 last are the sole variables when the wires are in an infinite 

 dielectric, or, else, are quite equal. By adopting the latter 

 course our solutions will consist of two parts, one expressing 

 very nearly the same results as if the differential effects did 

 not exist, the other the differential effects by themselves. 



Another result of inequalities is to produce inductive inter- 

 ferences from parallel wires which would not exist were the 

 wires equal. As an example, let an iron and a parallel copper 

 wire be looped, and telephones be placed at the ends of the 

 circuit. Even if the wires be well twisted, there is current 

 in the telephones caused by rapid reversals in a parallel wire 

 whose circuit is completed through the earth. Again, if two 

 precisely equal wires be twisted, and telephones placed at the 

 ends as before, the insertion of a resistance into either wire 

 intermediately will upset the induction-balance and cause 

 current in the terminal telephones when exposed to interfe- 

 rence from a parallel wire. This interference can be removed 

 by the insertion of an equal resistance in the companion -wire 

 at the same place. In the working of telephone metallic cir- 

 cuits with intermediate stations and apparatus, we not only 

 introduce great impedance by the insertion of the interme- 

 diate apparatus, thus greatly shortening the length of line 

 that can be worked through, but we produce inductive inter- 



G 2 



