344 



BELL SYSTEM TECHNICAL JOURNAL 



jump of 2/k. Thereafter we have a series of jumps of 2/k at time 

 intervals 2s /v, the current decreasing between successive jumps. 

 The smooth curve is the indicial admittance of an oscillation circuit 

 consisting of an inductance sL in series with a capacity Co- We see 

 therefore, that the current in the line oscillates with discontinuous 



l/VsLCo-OJ 



Multiply Ordinates by \^C7L 



sL= Tobal Inductance of Line 

 sC= " Capacity " " 

 C/ Terminal Capacit;/ 



Values of t/nViLC, 



0.5 



0.6 



Fig. 26 — ^Current entering non-dissipative line terminated by capacity C„ unit E.M.F. 



applied to line 



jumps about the current in the corresponding oscillation circuit. 

 Since the whole circuit contains no resistance, the oscillations never 

 die away, but continue to oscillate, as shown, about the curve 



^iHvku) 



which is the indicial admittance of the corresponding oscillation 

 circuit. 



I shall now discuss a method of solving circuit theory problems, 

 quite generally applicable to complicated networks, and particularly 

 useful in dealing with transmission lines terminated in impedances. 

 I have found it particularly useful in arriving at numerical solutions 

 where other methods prove far more laborious. It is also of mathe- 

 matical interest, as it applies another type of integral equation to the 

 problems of electric circuit theory. 



Suppose that we have a network with two sets of terminals as shown 

 in Fig. 27.'^ Now suppose that terminals 22 are short circuited and a 

 unit e.m.f. inserted between terminals 11. Let the resultant current 

 flowing between terminals 11 be denoted by Si\{t)=Sii and that 



' Regarding conventions as to signs, see the Appendix to this chapter. 



