INTERI-IIRENCE ON SUBMARINE TELBGR/WH CABLES 409 



problem. There is available, however, from a recent study of the 

 problem of the sea return resistance of a submarine cable, ^ information 

 that enables us to compare the behavior of xarious cable structures 

 from the point of view of shielding. One of the results of this work was 

 the determination of the degree to which the shielding effect of the 

 metallic sheath around the cable causes the returning signal current 

 to flow in this sheath rather than in the surrounding sea water. It is 

 obvious that the greater the tendency of the metallic sheath to confine 

 the return current to itself, the more effective the sheath will be in 

 reducing the pick-up of interference. Allowing for the two effects just 

 discussed, it is evident that the electromotive force induced in unit 

 length of the cable conductor is given by an expression of the form 



e^AEoe-''^ (2) 



where ^ is a multiplier, the value of which will be determined only on a 

 relative scale. 



The electromotive force induced in any section of the cable conductor 

 gives rise to sinusoidal currents and potentials which are transmitted 

 in both directions along the conductor in accordance with well-known 

 laws. For simplicity we will assume that the cable is terminated at 

 both ends in its characteristic impedance, Z, the result corresponding 

 to any other values of terminal impedances being readily determinable 

 if needed.^ Then an electromotive force e dx, induced in a short section 

 of cable of length dx, distant x from the terminal, will result in a current 



e dx 

 ~2Z 



—yx 



(3) 



at the terminal. If the electromotive force per unit length e is picked 

 up uniformly over a length of cable extending from x = a to x = s, then 

 since the impedance in each direction from the point is Z, the resulting 

 current at x = o will be 



2Z 1 



dx e-y'' 



(4) 



= f-ay ! 



2Z 7 



* Carson and Gilbert "Transmission Characteristics of a Sul)niarine Cable," Jour. 

 Franklin Inst., Vol. 192, p. 705, 1921, and Electrician, Vol. 88, p. 499, 1922; Bell Sys- 

 tem Technical Journal, Vol. I, No. 1, July 1922. 



* Heaviside, "Electromagnetic Theory," Vol. 2, p. 75. 



