520 BELL SYSTEM TECHNICAL JOURNAL 



Set 5 (Fig. 6) 

 {A) In the wire, a distributed electromotive force, f{x)dx in each 

 differential length dx. 



(B) In the distributed complete shunt admittance, a distributed 

 electromotive force, (Y'/Y)F(x) in each differential element Ydx of the 

 complete shunt admittance. 



(C) In the terminal impedances Zo and Zs, electromotive forces 

 F(0) and F{s) respectively. 



In Set 5 it should be noted that the electromotive force {Y'IY)F{x) 

 is in the complete shunt admittance element Ydx. 



It will be observed that Set 5 (Fig. 6) is the same as Set 1 (Fig. 4) 

 as regards the axial and the terminal electromotive forces. 



Set 6 (Fig. 11) 



(A) At any arbitrary fixed point x = a in the wire, an axial electro- 

 motive force Ga, 



(B) In each differential element Ydx of the distributed complete 

 shunt admittance, a distributed electromotive force Ex, 



£,= £[/(.) +^'^1^.. x<a. 

 £.= -f [/W+^'^]<ix, x>a. 



(C) In the terminal impedances Zo and Zs, electromotive forces 

 (1 - Y'IY)F{0) and (1 - Y'IY)F(s) respectively. 



Set 6 is perhaps mainly of academic interest. 



Two limiting cases of Set 6 may be noted, corresponding to a = 

 and a = s respectively, each characterized by containing no internal 

 axial electromotive force: for when a = the axial electromotive 

 force Ga can be combined with the terminal electromotive force 

 (1 — Y'IY)F{0) in the terminal impedance Zo, and when a = s it 

 can be combined with (1 — Y'IY)F{s) in Z,. 



Extension to the Case where the Impressed Potential is Discon- 

 tinuous 



In the foregoing formulations of Sets 1, • • • 6 of equivalent electro- 

 motive forces it has been assumed that the impressed potential F{x) 

 is a continuous function of x throughout the length of the line. 



Suppose now, for greater generality, that the impressed potential 

 F{x) is discontinuous at any point x = u by the increment 



AF{h) = F{u +) - F{u -). 



