514 BELL SYSTEM TECHNICAL JOURNAL 



of the current contribution originating in the direct leakage admittance 

 element Y'dy at y, which reaches point x. 



Case 2: Terminal Impedances Equal to Characteristic Impedances 

 Here we have 



Zo = Z, = K, (46) 



Aix, y) = TTE^ e-^^^^-y^ (47) 



IK. 



B(x,y) = T ^e-T'^-^, y ^ x, (48) 



whence 



j{x) =^f ^"^'"-^ f(y)dy (49) 





e-y^^-v)f{y)dy (50) 



+ 2^J^-^^^-^^/(3')'^3'- 

 ^o(x) = -j§e-y^, (51) 



/«(:^) =^e-y^^-'\ (52) 



/os(:x;) = J 



I ' F{y)e-y^'-^^dy (53) 



Jo 



Y' r 



+ ^ I F(y)e-y^y-^'>dy, 



Ju(x) = -^^^--'— . (54) 



^ Balanced Two-Wire Line in an Arbitrary Impressed Field 

 Because the metallic circuit here contemplated is balanced, its 

 treatment can be made formally the same as the treatment of the 

 one-wire line in the preceding subsection. 



This fact is immediately evident in two special cases of the impressed 

 electric field (potential and axial electric force) : (1) the case where the 

 impressed electric field has equal values at the two wires, and (2) the 

 case where it has equal but opposite values at the two wires. 



The general case where the impressed field at the two wires has any 

 values can be treated as a superposition of the two special cases just 



