66 TRANSMISSION LINE FORMULAS 



that is, j ^^- L r( P 2 LiX - P 2 x io~ + * 3 lo' 9 ) dx = o 

 r Jo 



Now LI is a constant, independent of x, and so 

 P 4 Z,! - P 4 io~ 9 + ^ io- = o. 



2 



Therefore LI = i X io~ 9 (5) 



The voltage drop between the wires A and J5 due to the 

 flux inside both wires is 



2j'wILi = 2/co/ X i X iQ" 9 volts per cm. 



= 270; X 80.47 X io~ 6 



volts per ampere per mile. The total reactive drop be- 

 tween the wires is thus 



2ju( 80.47 + 741.1 logio-J X io~ 6 (6) 



volts per ampere per mile of single phase line. 



This may be written in the following form which is more 

 convenient for computation by means of logarithm tables: 



Reactance drop = 2J<a X 741.1 logio - X io~ 6 (7) 



0.779 P 



volts per ampere per mile of single-phase line. 



The above is the usual formula for reactance of a single- 

 phase line. The proof is longer than that generally given, 

 but it has the advantage of giving a correct idea of 

 the distribution of current and magnetic flux inside the 

 wire. As the irregular distribution of current produces the 

 "skin effect" described in the next chapter, and necessi- 

 tates slight corrections in the above formula for reactance 

 and in the resistance, the importance of calculating the 

 correct current distribution is evident. The above formula 

 is sufficiently accurate, however, for calculating the tables 

 of reactance of wire in Part III. 



