738 BELL SYSTEM TECHNICAL JOURNAL 



much as 20 per cent. This section of the country has also the great- 

 est diurnal range of temperature, giving a d.-c. resistance variation of 

 as much as 8 per cent. 



Inductance 



The inductance of a circuit formed of two parallel wires whose dis- 

 tance between centers is negligible compared with their length is 



r 2D 



L = 0.64374 2.3026 logic ^ + a^S 



X 10~^ henrys per loop mile, (3) 



where the diameter of each wire d, and the distance between their 

 centers D, are expressed in the same units, where ix is the permeability, 

 and 5 is a factor depending on the frequency. 



The tendency of alternating currents to concentrate on the surface 

 of a wire evidently reduces the magnetic flux within the wire and de- 

 creases the internal inductance of the wire. In Equation (3) the in- 

 ternal inductance is represented by the factor nb. At low frequencies, 

 for which the current is uniformly distributed across the cross-section 

 of the wire, the value of b is 0.25. For very high frequencies there is 

 practically no magnetic flux within the wire, and the value of b is zero. 

 Between these frequency limits the value of b is determined with the 

 aid of skin effect formulas or tables.^ For the wire diameters and spac- 

 ings employed on open-wire lines the change in the total inductance 

 due to skin effect is relatively small. 



It is assumed in Equation (3) that the two wires are suspended in 

 space or at a considerable distance from the ground and from other 

 wires. In practise, the presence of other wires probably has some 

 effect on the inductance, but for well transposed lines this effect is 

 negligibly small. 



The inductance at different frequencies of 165, 128, and 104-mil 

 copper pairs having various spacings between wires is shown in the 

 following table. 



As will be seen from Equation (3), the inductance varies with the 

 logarithm of the separation between wires. In the table the values of 

 inductance are shown for pole pairs, which have a separation between 

 wire centers of about 18.25 inches, and for non-pole pairs having wire 

 separations of 12 and 8 inches. The values of inductance given in the 

 table have been closely checked by measurements on open-wire pairs. 



^ See, for example, Circular No. 74 of the Bureau of Standards, "Radio Instru- 

 ments and Measurements." 



