230 BELL SYSTEM TECHNICAL JOURNAL 



the ratio of the actual speed of propagation to the speed of light, i.e., 

 180,000 to 186,000 or about .97. Therefore ( 1 + ^ ) is about 1.94. 



\ TaTb / 



(4) Fa = N„.- N, = Nei—- A 



\ TaTb / 



AT- / n/C I • 90 Ofn + at \ 



= A^e I - .06 + 7 — — ^ — j approx. 



The attenuation of the disturbing and disturbed circuits may not be 

 neglected in evaluating the expression ( — ^- 1 ) • 



\ 7a76 / 



The expression given for Ne in equation (1) above may be written: 



^aTahW Ca Cft 



N.= - 



2K Ca Ca 



This assumes ZnjcoCa equals ja. At carrier frequencies 7a is about 

 equal to jl3a which is about JTrK/90 since the speed of propagation is 

 about 180,000 miles per second. The expression for Ne may, therefore, 

 be written in the following simple approximate form: 



_ _ . TrrgfelO'^ Ca Cb 

 ^ " ~ ^ 180 Ca' 'Ca' 



The ratio of C„ to C„' does not ordinarily exceed 1.02. For like 

 circuits, therefore: 



.. - jirTatW 

 ' = 180 approx- 



On Fig. S3 the magnitudes of Nd and Fd are plotted against frequency 

 for 8-inch spaced conductors .128-inch in diameter. Both Fd and A^^ 

 are divided by Tab to make the curves applicable to any circuit combi- 

 nation. These curves show that Na is practically independent of 

 frequency (above a few hundred cycles) but Fd decreases rapidly with 

 frequency for several thousand cycles. 



Indirect Crosstalk Coefficients 

 Expressions for the indirect crosstalk coefficients used in computing 

 the indirect component of transverse crosstalk coupling will now be 

 derived. The derivation first covers the case of a single representative 

 tertiary circuit. Fig. 34 shows a thin transverse slice of the parallel 

 of the three circuits, the thickness of the slice being the infinitesimal 

 length dx. The only tertiary circuit to be considered for the present 

 is the metallic circuit composed of wires 5 and 6 and designated as c. 

 There are other possible tertiary circuits in the system of 6 wires. 



