316 Mr. G. A. Campbell on Loaded 



the attenuation coefficient a, and the velocity of propagation 

 v, are given by 



k=<JJj~ . (2) 



v=«+ P iW% ■■■:■« 



where, if E, L, 0, S are the effective loop-line resistance, 

 inductance, capacity, and leakage conductance at a frequency 

 P/'2tt, the series and shunt impedances are 



j 1 =n+Lpt,, (4) 



^.(S+CpO" 1 '; (?) 



consequently 



«=^^|Rq_LV)(S 2 + 2 7)+i(RS-LC^ . (6) 



= .yA/TA 1 + -o ) for large L and small S . . (7) 



^OSTLS' ^ 



For transmission from one construction of impedance h x to 

 a sepond of impedance k 2 the current reflexion and trans- 

 mission coefficients are respectively 



_^1 ^2 



"-1 ~i~ ^2 



(9) 



1 + «=CT ("» 



If upon a line of length Z with terminal sets of impedances 

 J*, J r , at the sending and receiving ends, there is an im- 

 pressed force Ee'^, the current at distance x from the sending 

 set is 



._ Eg^ e-y~ + a r ey x - 2 y l 



where the reflexion coefficients are 



k-J r k-'J s 



If the line attenuation is large and the sending and re- 

 ceiving sets are similar, the receiving current is approxi- 

 mately 



