428 BELL SYSTEM TECHNICAL JOURNAL 



quencies. The critical frequency will be denoted by/t; also by /i — 

 particularly when regarded as the first transition frequency. The 

 relati\e frequency will be denoted by r, that is, 



r=f/fc=f'U (13) 



Evidently ri = 1. General formulas for all of the transition frequencies 

 are furnished a little further on. For the case of no distributed 

 inductance (L = 0), there is only one transition frequency — the 

 critical frequency — and it has the value expressed by equation (3). 

 When necessary for distinction, the critical frequency for the case 

 of no distributed inductance will be denoted hy f/, also by/i'; thus, 



/c'=/i'=l/^VlT. (14) 



The ratio of the critical frequency of any loaded line to the critical 

 frequency of the same loaded line without distributed inductance 

 (L=0) will be denoted b>- p; that is, 



P=Mc'=h/h'. (15) 



p can be evaluated by means of formula (22). 



It is convenient to employ the term "compound band" to denote 

 the band consisting of a transmitting band and the succeeding at- 

 tenuating band. It is shown in Appendix A that, for any specific 

 loaded line, the widths of all the compound bands are equal; though 

 the transmitting bands become continuallN' narrower witii increasing 



9 2-g- (n-i)-9 n^ 



Dq,) D,2 D2_3 Dn.,n Dn^n+i 



,., -tD attenuating band 



n transmitting band-* 



D»ia)"VLC 



n'" compound band 



Hjj. (j S(.il<- .Shouiiiy I Ik- Disposition of the Transmitting and the Attenuating 

 Bands of a IVrioilicaliy Loaded Line (Kig. 1) with Distributed Inductance 



frequency, while the attenuating bands become continually wider. 

 These facts are represented on the D-scale in Fig. 6, D being propor- 

 tional to the frequency /. Fundamentally D denotes the quantity 

 itoVLC; but, by the substitution of \ = L L'. and of r and /> defined 

 by (13) and (1.5), D can be written in the following four identically 

 equivalent forms: 



D = ia)V'IC=Ja.\/XZ7C = r/>\/x = /-£>,. (16) 



