90 BELL SYSTEM TECHNICAL JOURNAL 



(4) At relatively high frequencies, the return impedance, and 

 hence the attenuation and the distortion, may be very greatly de- 

 creased by a correctly designed thin metallic sheath concentric with 

 the core, and in electrical contact with the armor wires. The very 

 important action of such a sheath, even when extremely thin, does not 

 appear to have been adequately recognized or studied. It is suggested 

 that the introduction of such a sheath alifords a means of greatly 

 increasing the range of frequencies which the cable can transmit. 



The general problem of determining the transmission character- 

 istics of a system consisting of an insulated conductor surrounded by a 

 concentric ring of armor wires immersed in sea water is of consider- 

 able difficulty, since in this case the propagated wave must be repre- 

 sented as a set of component waves centered upon or diverging from 

 the axes of the core and of the individual armor wires. The problem 

 was first simplified by replacing the ring of armor wires by a cylindrical 

 sheath, thus giving circular symmetry to the structure. The analysis 

 of this case, however, showed that the effect of the iron sheath re- 

 placing the armor wires was so pronounced as to make this simplifying 

 assumption of doubtful validity. The general problem was there- 

 fore attacked, and rigorous methods developed for calculating the 

 effect of the armor wires upon transmission. The results in this 

 case differ markedly from those obtained for the case of a continuous 

 iron sheath, which indicates that great caution must be used in making 

 assumptions regarding the physical structure of the armoring. 



The present paper follows rather closely the course of the writers' 

 investigation. In Section II is analyzed the problem of transmission 

 over a system consisting of n coaxial cylindrical conductors, which 

 may be either in electrical contact at their adjacent surfaces or sepa- 

 rated from each other by dielectric spaces. The outermost con- 

 ductor, consisting of the sea water, is assumed to extend to infinity. 

 This analysis is then applied, in Section III, to the case of a sub- 

 marine cable which is armored with a continuous iron sheath. This 

 problem is not only of interest in itself, but serves as a first approxi- 

 mation to the case of an actual cable, and gives a clear qualitative 

 idea of the effect of the various factors on transmission. In Section 

 IV the problem of the submarine cable armored with a ring of iron 

 wires is attacked and solved by rigorous methods, and the theoretical 

 results are then compared with experimental data. 



II 



The solution of the problem of transmission of periodic currents 

 over a system comprising n coaxial cylindrical conductors consists 



