350 BELL SYSTEM TECHNICAL JOURNAL 



which determines iii since iio is known. Simihirly 



n2=fo-\-d [huoki-'rUiki + hniko] 

 which delerniines u^. Proceeding in the same manner 



ii3=f:i-\-d [^/(„^.-! + ''i^2 + ''2^i + 2^';i^o], etc. 



In this way we determine the value of u{x), point l)y point from the 

 recurrence formula 



nn = 



f„ + d{\Uokn + Ulkn-\+tl2kn-2-\- • ■ +Un-\ki\ 

 1 — hkod 



(266) 



The result of the application of numerical integration, in accordance 

 with formula (266), to the integral equation (263) is shown in Fig. 

 (29). The dotted curve is a plot of the approximate solution as 



Fig. 29 — Line terminal voltage unit E.M. F. im pressed on line through resistance 



Ro = VL/C 



given by equation (264), for a = l. We see that the voltage starts 

 with the value 1/2 and slowly reaches its ultimate value, unity, 

 its approach to unity, for large values of /, being in accordance with 

 the formula 



F(0= ^—7=- 



l + l/\/27r/ 



The application of the foregoing method to the transmission line 

 problem proceeds as follows. Let 5'n(/), 522(0 and 6'i2(/) be the 

 short indicial admittances of the line. 5u(/) is the current entering 

 the line (at .r = 0) with unit e.m.f. directly impressed and the distant 

 end short circuited. Sn{t) is the ciirrent at x = s under the same 



