736 BELL SYSTEM TECHNICAL JOURNAL 



close agreement with the values given in Fig. 5.* For old wires, 

 however, the resistance may be somewhat higher than these values. 

 This is because of the presence of contact resistance in the twisted 

 sleeve joints in the wires and also perhaps because of an actual decrease 

 in the conductor diameter occasioned by corrosion. The increase in 

 the d.-c. resistance of old wires due to these causes may be as much as 

 5 per cent. The corresponding percentage of increase in the a.-c. resis- 

 tance will, of course, be much smaller. The d.-c. resistance of a copper 

 wire varies with temperature according to the familiar formula: 



Ro = Roi [1 + ai (^ - k)], (1) 



where Ro and Roi represent the d.-c. resistance at temperatures / deg. 

 cent, and h deg. cent, respectively, and ai is the d.-c. temperature 

 coefficient of resistance of copper at /i deg. cent. At a temperature of 

 20 deg. cent, the value of ai is generally taken as 0.00393. 



Similarly, the a.-c. resistance R of a copper wire at a temperature / 

 may be represented as follows: 



R = RAi +^i(/-/i)], (2) 



where Ri = a.-c. resistance at temperature /i deg. cent., 



. 1 dR ,-,, . p . p 



Ai = ^ -jT = a.-c. temperature coerhcient oi resistance ol copper at 

 Ki at 



ti deg. cent. 



Now the skin effect resistance ratio depends upon the magnitude of 

 the d.-c. resistance, being smaller the larger the resistance. Hence, 

 a given change in temperature which changes the d.-c. resistance pro- 

 duces a change in the opposite direction in the skin effect resistance 

 ratio, so that the percentage change in the a.-c. resistance is less than 

 the percentage change in the d.-c. resistance. In other words, Ai is less 

 than a\. As illustrated in Fig. 6, the a.-c. temperature coefficient of 

 resistance for open-wire pairs, starting at the d.-c. value ai, straight- 

 way decreases as the frequency is increased, and at high frequencies 



approaches a value of— . An explanation for this asymptotic value is 



presented in Appendix I. 



The temperature assumed by the conductors of open-wire lines de- 

 pends of course, upon the weather conditions which prevail in different 

 sections of the country. In order to obtain information on this subject, 



* The value of R, and also that of the other primary constants, may be determined 

 directly from open and short-circuit impedance measurements on a line short enough 

 to avoid propagation effects. A longer line may be used instead, in which case it is 

 necessary to correct for such effects. 



