54 



BELL SYSTEM TECHNICAL JOVRX.IL 



Its subsidence to its final zero value is very slow; for example, when 

 T = 100 its value is still 



2 



\ 



/tt xR 



(0.10). 



Turning to the voltage curve, Fig. 4, we see that it is negligibly 

 small until r reaches the value 0.25, at which point it begins to build 

 up. Its maximum rate of building up occurs when t = 2/3, after 



ni2345 6789(0 



Fig. 5 — Power transmitted in non-inductive cable (G = 0) 



which it builds up more and more slowly. Its approach to its final 

 steady value is in accordance with the formula 



F-1 



1 



.1+1 A 



Even, therefore, when r is as great as 100, V differs sensibly from its 

 ultimate value, unity, its value being 0.8876. 



2 J? n 

 Since the actual time is '—7— r, it follows that the speed of building 



4 



up is inversely proportional to the square of the length of the cable. 



The power curve VI is given in Fig. 5. V.I is the rate at which 

 energy is being transmitted past the point x of the cable. 



The fact that the form of the current and voltage waves depends 

 only on Ujx^RC is at the basis of Kelvin's famous "KR" law, long 

 applied to cable telegraphy and sometimes incorrectly applied to 

 telephony. When the first transatlantic telegraph cable was under 

 consideration, Kelvin attacked the problem of propagation along the 

 non-inductive cable and arrived at formulas equivalent to (169) and 



