KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 99 



of Figure 2, and that the capacity in each section of Figure 1 

 should be twice the capacity in each section of Figure 2 ; so that 

 the CR product, i. e. the total resistance R 

 in the line circuit and the total capacity C j^ 



across the circuit, shall be the same. The 

 double-conductor line of Figure 2 has, there- 

 fore, twice the total resistance, and half the 

 total capacity, of the single-conductor line of 

 Figure 1 for the same electrical retardation, 

 and is thus the cheaper type to build, for 

 a given CR. Since, then, to any double- 

 conductor line of Figure 2 there is always a 

 corresponding electrically equivalent single- 

 conductor line of Figure 1, and the latter is, 

 perhaps, the simpler to analyze and discuss, 

 we may confine our attention entirely to the 

 single-conductor or ground-return-circuit 

 artificial line. 



Fundamental Relations and 

 Notation. 



The continuous-current type of single- 

 conductor artificial line is indicated in Fig- 

 ure 3. Let there be m sections. In the case 

 presented, m = 4. Let each section repre- 

 sent a nominal length, I, kilometers (or 

 miles) of line, and have a conductor resis- 

 tance of / ohms. Let the leak connected 

 to the centre of each section have a conduc- 

 tance of q' mhos and a resistance of R' = — 

 ohms. Let the total nominal length of the 



line be L = ml kilometers and let A. = - be 



2 



the nominal length of a half section in kilo- 

 meters. 



First determine the nominal or apparent 

 attenuation-constant of the artificial line as 



though the resistance and leakance were distributed as in an actual 

 line: 



