198 BELL SYSTEM TECHNICAL JOURNAL 



transposition section since this is ordinarily small. It also assumes 

 that the rule for locating transposition poles, that is, that S^ should 

 not exceed kL2, is applied for lengths having only negligible attenuation. 

 In making estimates of R in connection with transposition design 

 work, it is assumed that all the segments are nominally the same 

 length, D, and that r is the r.m.s. value of the deviations of the seg- 

 ments. Since r^ equals S^ divided by the number of segments in 

 length La, r"^ should not exceed kD. B} may be expressed approxi- 

 mately in terms of r- as follows: 



1 - €-^«^ 



i?2 = ^2 



\ _ g-4aZ> > 



where R and r are expressed in the same units, L is the length of the 

 line in miles, a is the attenuation constant per mile, and D is the 

 segment length in miles. If the line loss is 6 db or more the expression 

 is nearly equal to: 



^2 



i?2 = 



.46Z)a ' 



where a is the line loss in db per mile and D is the segment length 

 in miles. This assumes 4q:Z) is small compared to unity which is 

 usually the case. 



The chance that the total unbalanced length will exceed about 

 l.XR is estimated at 1 per cent. 



For far-end crosstalk (output-to-output) the same assumption as to 

 nominal segment length leads to the expression: 



R 



■Ji,- 



The general expressions given for R^ suggest that a very long 

 segment might be permitted at some point in the line if the deviations 

 of the segments were properly restricted in other parts of the line. 

 The expressions given for far-end and near-end values of R^ were 



i?2 = Si" -f Si'A,^ + 53^2^ + • • •. 



If a very long segment at some point, such as a river crossing, were 

 permitted, this would increase the sum of the squares of the deviations 

 for some transposition section. For example S3 might be abnormally 

 large. R^ could be kept at some assigned value by limiting Si^, Si^, etc. 

 This procedure is not considered good practice because of the difficulty 

 of maintaining some parts of the line with very small deviations of 

 the segments from their nominal lengths. 



