TRANSMISSION OVER SUBMARINE CABLES 89 



plexity and involve rather difficult analysis. In the case of the sub- 

 marine cable, exact formulas are available for calculating the capacity 

 and leakage and the core impedance. Considerable uncertainty is 

 introduced into the theory, however, on account of the lack of a 

 method of determining the "return impedance," that is, the con- 

 tribution of the "sea return" (sea water, armor wires, etc.) to the 

 effective resistance and inductance of the circuit. An investigation 

 of this problem was undertaken by the writers in connection with the 

 research program of the American Telephone and Telegraph Company 

 and the Western Electric Company. 



The purpose of the present paper is to discuss transmission over 

 the submarine cable, and, more particularly, to develop rigorous 

 formulas for the calculation of the impedance of the return con- 

 ductor of the cable. The results of theoretical calculations are then 

 compared with actual experimental data; and the agreement between 

 theory and experiment is so satisfactory as to indicate that the former 

 is a reliable guide in the design and predetermination of the cable. 



Besides providing a method for accurately calculating the trans- 

 mission characteristics of a submarine cable, the present analysis 

 leads to the following general conclusions: 



(1) Contrary to usual assumption, the "sea return" impedance 

 is by no means negligible. Even at quite moderate frequencies there 

 is a considerable crowding of the return current into the immediate 

 neighborhood of the cable, with a consequent rapid increase of the 

 resistance and a corresponding decrease of the inductance of the 

 circuit. Except at the lowest frequencies, therefore, the impedance 

 of the "sea return" is a very important factor. 



(2) The armor wires which surround the cable, and which are 

 necessary for mechanical protection, have a very pronounced effect 

 on the impedance of the sea return, and even at moderate frequencies 

 may become the controlling factor. Their action is to screen the 

 current from the sea water itself, and, as the frequency increases, 

 to carry more and more of the return current, until it is almost en- 

 tirely confined to the armor wires and excluded from the sea water. 



(3) The rapid increase in the impedance of the armor wires with 

 frequency, and their pronounced and even controlling effect on trans- 

 mission makes a thorough-going study of their role in the electrical 

 system a matter of first-class importance. Heretofore they appear 

 to have been regarded only as a mechanical protection, and their 

 effect on transmission has been ignored. The accurate method of 

 calculating their impedance which is developed in the following pages 

 is believed to have considerable value in this connection. 



