PROPAGATION OF PERIODIC CURRENTS 519 



Set 4 (Fig. 8) 



(A) In the wire, a distributed electromotive force, [/(x) + (Y'/Y) 

 X dF(x)/dx2dx in each differential length dx. 



(B) In the terminal impedances Zq and Zs, electromotive forces 

 (1 - r/Y)FiO) and (1 - Y'IY)F(s) respectively. 



Set 2 is distinguished by containing no electromotive forces in the 

 shunt admittance even when the direct leakage admittance Y' is not 

 negligible. Thus Set 2 with the direct leakage admittance not negli- 

 gible is formally as simple as Set 1 with the direct leakage admittance 

 negligible. However, in Set 2 the element of axial electromotive force 

 is a much more complicated function than in Set 1. 



Set 3 (Fig. 9) 



(A) In the wire, a distributed electromotive force, [/(.%") + 

 dF{x)/dx2dx in each differential length dx. 



(B) In the distributed basic shunt admittance, a distributed elec- 

 tromotive force, — F(x) in each differential element Y^dx of the 

 distributed basic shunt admittance. 



In Set 3 it should be noted that the electromotive force — F{x) is 

 in the basic shunt admittance element Y'^dx, not in the complete shunt 

 admittance element Ydx. 



It will be observed that this set contains no electromotive forces 

 in the terminal impedances. 



When the ground is a perfect conductor, so that fg(x) = 0, the 

 differential element of axial electromotive force in this set reduces to 

 merely — \^d^(x)ldt~\dx, as is shown by equation (2) of Appendix I, 

 $(jc) denoting the impressed magnetic flux. 



Set 4 (Fig. 8) 



(A) In the wire, a distributed electromotive force, [/(.v) + (1 

 + Y'/Y)dF(x)ldx^dx in each differential length dx. 



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

 electromotive force, — F{x) in each differential element Ydx of the 

 complete shunt admittance. 



(C) In the terminal impedances Zq and Z^, electromotive forces, 

 - (F7F)F(0) and - {Y'/Y)F{s) respectively. 



In Set 4 it should be noted that the electromotive force — F(x) 

 is in the complete shunt admittance element Ydx. 



The differential element of axial electromotive force in this set does 

 not reduce to — \^d^(x)ldQdx when the ground is a perfect conductor 

 (/sU") = 0) unless also the direct leakage admittance is zero (F' = 0). 



34 



