78 TRANSMISSION LINE FORMULAS 



and 2j*to) dx = o. 



o 



Substituting the value of i( X ) from the first equation, we have 



dx 2>(z)C( X ) dx 10 8 = o. 

 o o 



Now ILi is a constant, and 



.' - A ' 



the area of the section of the cable. 



By dividing p into a number of equal parts and calling 

 each part dx, the value of 4>( X )C (x} dx for each successive 

 value of x is found. Adding these together, a close estimate 



of the value of 



p 



JV<( X )C( X ) dx 

 IT 



is obtained. This, divided by I A gives the value 



Li = 0.633 X io~ 9 . 



If the conductor were a solid wire of radius p, with a 

 straight line curve of / (x) , L\ would be \ X lo" 9 , which 

 would become 80.5 X io~ 6 when reduced to the ordinary 

 formula for reactance per mile. Thus the reactance per 

 mile of cable is 



x = So.s X 4- 741-1 log w -) io- X 2 TT 



0.500 pi 



102 + 74I.I logio- I0~ 6 X 2 IT/ 



ohms per mile. 



The same process applied to a ig-wire strand gives the 

 formula 



x = ( 89 + 741.1 logio-j lo" 6 X 2 TT/ 

 ohms per mile. 



