KENNELLY. — ARTIFICIAL LINES FOR CONTINUOUS CURRENTS. 119 



although the internal distributions of voltage and current differ, the 

 external distributions are identical. That is, the distribution of voltage 

 and current at the ends of, and anywhere external to, the artificial 

 line are identical for the single-section artificial line of Figures 13, 14, 

 and 15; or for the five-section artificial line of Figures 5, 6, and 7; or 

 for the actual smooth uniform line of a = 0.0035172 hyp. per km. 

 and r = 1436.1 ohms, there imitated. 



For brevity and convenience, let a single-section artificial line, like 

 that of Figure 14, formed of a conductor-resistance / ohms, with a 

 leak of R' ohms at the centre, be called a T, from the graphical resem- 

 blance. Then, any real smooth uniform line may be replaced by its 

 equivalent T, without any change in the electrical system external to 

 the T, after the steady state has been attained. This proposition, like 

 the rest, applies not only to a continuous-current system, but also to 

 any single-frequency alternating-current system. 



In duplex and multiplex telegraphy, artificial lines are required to 

 balance real lines, not only in the steady state, but also in the preced- 

 ing unsteady state ; so that it is not possible to employ an equivalent 

 T for such artificial lines. In telephony, however, it is commonly 

 believed that the electrical phenomena in ordinary conversation are 

 substantially steady state single-frequency phenomena, and that the 

 conditions in the unsteady state are so transient that they may be 

 practically ignored. If this is correct, then it follows that, except for 

 purposes of adjustment, and of convenience in altering the length of 

 line, there is nothing to be gained by employing a multisection arti- 

 ficial line for embodying the laboratory equivalent of an actual line. 

 In other words, a single-section artificial line of properly selected 

 constants should be just as good as a multisection artificial line, in 

 regard to carrying on conversation. It is important to have this 

 question settled experimentally. The experiment, if unsuccessful, 

 cannot, however, be competent to determine whether the unsteady 

 state enters appreciably into the phenomena of practical telephonic 

 transmission, owing to the presence of multiple frequencies or 

 harmonics. 



Conversely, if we have a given T line, we can determine its hyper- 

 bolic angle and surge-resistance ; that is, we can determine the actual 

 smooth uniform line to which it corresponds; for in Figures 10 

 and 11 



sinh 6 = sinh \a - \ -^-, (82) 



and r = V P '( P ' + 2R') ohms. (83) 



