366 BELL SYSTEM TECHNICAL JOURNAL 



P becomes negligible, that is, the crosstalk is practically all due to the 

 component which exists in the complete absence of a sheath (see 

 equation (1)). In the range of lengths where this is true the crosstalk 

 increases directly with length. 



Quite a different state of affairs exists for a section electrically long 

 enough for equation (6) to hold. The first bracketed term is still 

 proportional to length but now consists of the difference of two com- 

 ponents. The first of these represents the crosstalk between the 

 coaxials with no sheath present while the second is a part of the crosstalk 

 component introduced by the presence of the sheath. Except for the 

 factor 74^74^ — 7^ this first bracketed term in equation (6) is the same 

 as equation (4) for a sheath in contact where, as we have already noted, 

 the cancellation of the two components is quite effective when steel 

 tapes are used on the outer conductors. Since y^ is necessarily con- 

 siderably greater than 7^ because of these steel outer conductors, it is 

 reasonable to expect that the factor y/^jy^ — y^ is nearly unity and 

 that, therefore, the two components in the first bracketed term of 

 equation (6) will also tend to cancel leaving a residual proportional to 

 length but much lower in magnitude than either component alone. 



The second bracketed term of equation (6) is entirely independent 

 of length. This term has also been introduced by the presence of the 

 tertiary circuit and its magnitude depends on the characteristics of 

 this circuit. 



Thus, even without knowing the relative magnitudes of the two 

 components of the first bracketed term of equation (6) for a given 

 length, it is apparent that as / is increased this term must eventually 

 be controlling. The crosstalk will then again be proportional to length 

 as it was for very short lengths but at a reduced level proportional to 



It is quite evident, too, that for a range of lengths where the tertiary 

 circuits are electrically long but where the first term of equation (6) 

 has not had a chance to build up sufficiently the crosstalk will be about 

 constant at a level determined mainly by the second term. 



The above analysis may well suffice as a background for an interpre- 

 tation of the measurements to be given in Part II. However, another 

 and perhaps in some ways a more illuminating approach from a physical 

 standpoint is possible. 



