568 BELL SYSTEM TECHNICAL JOURNAL 



is the same for any point in the section, but it is somewhat simpler 

 to assume that the additional capacity is applied at mid-section. 



The reactance of the added capacity is - and the luid-stTiioii 



2jr//icC 



k 

 impedance is, closely, / 



When the bridged reactance is large compared with the line im- 

 pedance, the reflection coefficient r^ is given closely by the equation 



k 



1 



''c = 5 ^ (12) 



2TTfhcC 

 from which, substituting the values of/ and k as before 



which is identical in form with equation (11) above. 



Approximations Made in Deriving rz, and Rc 



The expressions for the mid-coil and mid-section impedances used 

 above in deriving equations (10) and (12) are simple approximations 

 which take no account of the effects of the resistance of the line 

 conductors and loading coils, leakage between conductors or dis- 

 tributed inductance. The errors due to these effects are negligible 

 in the important parts of the frequency range involved in telephone 

 transmission when the types of loading and sizes of conductors now 

 commonly used are considered. The errors due to these causes tend 

 to increase for frequencies which are very low or which approach the 

 cutoff frequency. For accurate calculations relating to very light 

 loading applied to high resistance conductors it would be desirable 

 to take into account the effects of resistance. Because the use of 

 the precise expressions would greatly com[)licate this discussion 

 and would probably serve no very useful pur|)ose at this time, the 

 approxiinations given above are used. 



Current Retirnkd to the .Sknuini; Knd of the I.ine 



Consider first a line having only one kind of irregularity' as, for 

 example, one in which only the loading coils are assumed to vary 

 from their normal values. If a current h enters such a line, a current 



