34 BELL SYSTEM TECHNICAL JOURNAL 



quads of the other group), at every splice but one. This particular 

 splice, near the middle of the cable, is known as the "transposition 

 point." At this splice the two groups are "transposed," that is, outer 

 layer quads are spliced to inner layer quads and inner layer quads 

 are spliced to outer layer quads. In this way the differences in 

 resistance and capacitance to ground of outer and inner layer quads 

 are averaged at the "transposition point" for each group. The 

 average resistance or capacitance to ground of a conductor of the outer 

 layer group will therefore dififer appreciably from the average resistance 

 or capacitance to ground of a conductor of the inner layer group. 

 The constants given in Table 1 are for a cable of this type. 



As in the case of the non-transposed cable, it is necessary to calculate 

 values of b for different lengths of line. Up to the transposition point 

 the procedure is the same as above, viz., 



Zii = Zoi coth Pih, 



where the subscript denotes the first section adjacent to the measuring 

 station. As soon as the point of open falls on the distant side of the 

 transposition point, where the conductor changes layers, the calcula- 

 tion of Zi is a composite one. That is 



Zin = Zoi tanh {PA + 5), (2) 



where Z/12 is the combined input impedance, Zoi is the characteristic 

 impedance of the adjacent section. Pi and /: its propagation constant 

 and length respectively, and 



h = tanh~i -^ — , 



where Zn is the input impedance of the distant section calculated from 

 the formula 



Zii = Z02 coth P2/2. 



However, the calculation of formula (2) involves practical diffi- 

 culties, and it is best reduced as follows: 

 Denoting PA as Qx and P'^i as Qi, 



and expanding, 



Zin = Zo\ tanh ( Qy + tanh 



_Zn 

 1 + tanh ^1 



,Zn\ 

 ZoxJ' 



Ziit — Zo\ 



tanh ^1 + „ 



\Zo) . 



