THEORY OF CONVERGENT SERIES 99 



Let EI = voltage of line at a distance / from the re- 



ceiver end, 

 and let Ii = Pi~jQi 



= current in the line at a distance / from the 



receiver end. 



(Since I t is usually not in phase with the voltage, it 

 must be expressed as a complex quantity.) 



Now in an element of length, dl, of the line, the voltage 

 consumed by impedance is 



The current consumed by admittance is 

 dl l = yE4L 



Thus ^ = zl l9 (i) 



and " '"; = yi. _ 



Differentiating (i) 



dl 2 dl 

 Substituting (2) in this gives 



This is a differential equation of the second order and 

 may be expressed in the form 



(D* - yz) E l = o, 

 and we have 



E l = A# lV "+A#- l * r (4) 



and from (i), 



(5) 



