I'iOli THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



Substituting (111) into (113) and integrating under the condition that at 

 7; = 0, ^ = and f = 0, we find 



^ , . {h - h')Aa 2 / 

 I — rjCtna + — -, rr— CSC a 



(m- 1) 



^ , . (h - h') 

 f — etna 7^ (p 



1 



1 



_{h + r^y-' /i^-ij ' 



1 



{v - I) [.{h + r))'-^ h"-'} 



(114) 



These equations describe the space curve formed by the cable in the 

 cross-current stratum. 



To determine the distances d and e (Fig. 32), we transform (114) for 

 the cable configuration to coordinates ^' and f' oriented along the ship's 

 path and normal to it respectively ])y means of 



I' = ^ cos v? — f sin <p, 



f ' = ^ sin V? + r cos ip. 



The result to terms of the first order is 



./ , , , {h - h')Aa 2 / 



I = rjCtna + — -. r— CSC a 



(m - ly 



^, (,1s ctna'(/i — h') 



f = V' I '/-tna + 



1 



1 



1 1 



) 



[y - 1) L(^ + nY'^ h^-'. 

 h' and denoting the corresponding values of ^' and f'; 



Letting r} = 

 by — c? and —e respectively, we obtain (52). 



ACKNOWLEDGMENTS 



Space does not allow the author to thank individually the many per-i 

 sons who offered comments, corrections, and information during the 

 preparation of this paper. He is especially grateful however to C. HJ 

 Elmendorf and H. N. Upthegrove who instigated the study and provided' 

 encouragement and support during its preparation, to R. C. Prim and 

 S. P. Morgan for critical comments on the manuscript, to B. C. Heezen 

 for oceanographic information, to A. G. Norem, R. L. Peek, and J. F. 

 Shea for the use of excellent unpublished earlier work on the problem, 

 to D. Ross for assistance on cable hydrodynamics, and to N. C. Young- 

 strom for invaluable consultations on practical aspects of the submarine 

 cable art and for his collaboration on the work in Appendix B. 



REFERENCES 



1. W. H. Thomson (Lord Kelvin), On Machinery for Laying Submarine Tele- 

 graph Cables, The Engineer, 4, pp. 185-186, Sept. 11, 1857. 



