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BELL SYSTEM TECHNICAL JOURNAL 



derived from (17) supplemented by (14). Formula (23) is valid 

 also when w = 1, with Di evaluated from one of its appropriate formu- 

 las; the resulting formula for the critical frequency /, =/t reduces to 



/,=/, = /,VX, w\/LC = p,w\/L'C = pfc' = pfi, 



(24) 



because Di=pvk,by (16); it is seen that (24) is consistent with (15). 

 For use in (24) and for certain other purposes to be met later, Fig. 7 

 gives graphs oi l—p, calculated by (22) and also (22.1), for a wide range 

 of X. Up to the present time the largest value of X occurring in prac- 

 tical applications in the Bell System is about 0.12; Fig. 7 covers 



1.0 



.9 1.0 1.1 1.2 1.3 



.1 .2 .3 .4 .5 .6 .7 

 X 



•"iy. 7.1 — Craplis for I'inilini; llu- Wiilllis i)f llu' riMiisniill iiii; M.uii 



-4 

 ■5 

 6 

 -7 

 8 



00 



about eight times this range. Inspection of it shows lliat the graph 

 of \—p is sensijjly a straight line up to values of r somewhat larger 

 than even 0.12; and that \—p is only slightly less than X/6, which is 

 merely the first term in the i)ower series formula for \—p obtained 

 from (22). 



The gra|)hs in Fig. 7.1 — constructed by means of formulas (22.1), 

 (22), (21) — represent directly the dependence of the /3-width t„ = 

 D„ — D„-y„ of the wth transmitting band on X and ii, for a wide range 

 of X and the first eight values of //. The /-width is then obtainable 



