604 



BELL SYSTEM TECHNICAL JOURNAL 



12 4 6 8 10 12 14 16 18 20 22 24 26 



NUMBER OF SINGING PATHS 



Fig. 3 — T{N, T) in perfectly regular circuit. 



tribution function of the active return losses toward the east is 

 ■512 + Sf (not including path G), the distribution function of the two 

 return losses in series around the repeater will be ^u + Sn + Sp as 

 derived in Appendix II. In the general case, there will be gain in 

 series with the active return losses, which may be considered as part 

 of the return losses. For convenience, define ^n as follows: 



Sx, = Si- F{Nu T) 



(1) 



Si and F{Nu T) are as discussed above; Ni is the number of repeater 

 sections towards the west end of the circuit ; and Gc is the gain of the 

 repeater in the west to east direction, say. Similarly, 



5i2 = Si- F{N,, T) - gc. 



(2) 



