26 BELL SYSTEM TECHNICAL JOURNAL 



tertiary circuit into another slice and then crosstalk from tertiary 

 circuit to disturbed circuit. 



The notion that there is only transverse crosstalk within any one 

 "thin slice" implies that the slice thickness corresponds to a distance 

 along the line of only infinitesimal length. If this distance were finite 

 it would correspond to a series of "thin slices" having interaction 

 crosstalk between them. Practically, however, if the distance along 

 the line corresponds to a line angle of five degrees or less, the interaction 

 crosstalk in this length is small compared with the transverse crosstalk. 

 A five degree line angle corresponds to a length of about .1 mile at 

 25 kilocycles, .05 mile at 50 kilocycles, etc. A transposed line is 

 divided into short lengths or segments by the transposition poles and 

 the line angle of these segments is ordinarily less than five degrees at 

 the highest frequency for which the transposition system is suitable. 

 Therefore, the crosstalk coupling between such transposed circuits 

 may be computed on the basis of transverse crosstalk wuthin any 

 segment and interaction crosstalk between any two segments. 



As shown by Fig. 2 the interaction effect involves the four compound 

 couplings: 



nacflcb, nacfcb, facncb, facfcb- 



The near-end crosstalk couplings Hac and Ucb of Fig. 2 are usually 

 much larger than the far-end couplings fac and fcb. The reason for 

 this, as discussed in Appendix A, is that the electric and magnetic 

 fields of the disturbing circuit tend to aid each other in producing 

 near-end crosstalk coupling such as Uac, and to oppose each other in 

 the case of far-end coupling such as fac For this reason the compound 

 coupling Hacficb is the most important and is usually the only compound 

 coupling which requires consideration in transposition design. Since 

 the path n„cncb results in a crosstalk current at the far end of the 

 disturbed circuit, it is in connection with far-end crosstalk between 

 long circuits that this matter of interaction crosstalk is important. 

 Far-end rather than near-end crosstalk coupling is controlling in 

 connection with open-wire carrier frequency systems for the reasons 

 explained below. 



Figure 3A indicates very schematically two one-way carrier fre- 

 quency channels routed over two long paralleling open-wire pairs. 

 The boxes at the end indicate the repeaters or terminal apparatus and 

 the arrows on these boxes the direction of transmission of this appa- 

 ratus. Transmission from the left on pair a results in near-end and 

 far-end crosstalk into pair b, as indicated by the couplings riah and fab. 

 The near-end crosstalk current cannot pass to the input of the terminal 



